Axial Anomaly for Eguchi-Hanson Metrics with Nonzero Total Mass

We compute the Dirac indexes for. the two spin structures kappa(0) and kappa(1) for Eguchi-Hanson metrics with nonzero total mass. It shows that the Dirac indexes do not vanish in general, and axial anomaly exists. When the metric has zero total mass, the Dirac index vanishes for the spin structure no, and no axial anomaly exists in this case.

Existence of complementary pairs of proportionally balanced designs

Proportionally balanced designs (pi BDs) were introduced by Gray and Matters in response to a need for the allocation of markers of the Queensland Core Skills Test to have a certain property. Subsequent papers extended the theoretical results relating to such designs and provided further instances and general constructions. This work focused on designs comprising blocks of precisely two sizes, and when each variety occurs with one of precisely two possible frequencies. Two designs based on the set V of varieties are complementary if, whenever B is a block of one, then its complement with regard to the set V is a block of the other. Here we present necessary conditions for the existence of complementary pairs of such pi BDs and provide lists of some restricted parameter sets satisfying these necessary conditions. The lists are arranged according to the number of blocks. We demonstrate that not all of these parameter sets give rise to designs. However we establish by construction of the sets of blocks that, for every feasible number of blocks less than or equal to 100, with the possible exception of 63, there exists at least one pair of complementary pi BDs. We also investigate the conditions under which the complementary design can be isomorphic to the original design, and again provide a list of feasible parameters for pairs of such designs with at most 400 blocks.

A(n-1) Gaudin model with open boundaries

The A(n-1) Gaudin model with integrable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding Bethe ansatz equations are obtained. (c) 2005 Elsevier B.V. All rights reserved.

Towards a profitable and sustainable future for grain growers: A professional development model for farm partners

Many Australian grain growers need to change their management approach to ensure their continued viability, but do not have the required knowledge and skills. Uptake of relevant education and training is poor, despite the positive correlation between learning, change and farm viability. As men are generally occupied with the operational aspects of the farm, much of the management role has been taken on by their partners, despite their lack of relevant formal qualifications. Professional development of farm partners therefore has the potential to improve the viability of grain growers. A model combining learning circles and action learning projects is proposed.

Effects of acetate and propionate on the performance of a photosynthetic biofilm reactor for sulfide removal

The effects of acetate and propionate on the performance of a recently proposed and characterized photosynthetic biological sulfide removal system have been investigated with a view to predicting this concept's suitability for removing sulfide from wastewater undergoing or having undergone anaerobic treatment. The concept relies on substratum-irradiated biofilms dominated by green sulfur bacteria (GSB), which are supplied with radiant energy in the band 720 - 780 nm. A model reactor was fed for 7 months with a synthetic wastewater free of volatile fatty acids (VFAs), after which time intermittent dosing of the wastewater with acetate or propionate was begun. Such dosing suppressed the areal net sulfide removal rate by similar to50%, and caused the principal net product of sulfide removal to switch from sulfate to elemental-S. Similarly suppressed values of this rate were observed when the wastewater was dosed continuously with acetate, and this rate was not significantly affected by changes in the concentration of ammonia-N in the feed. The main net product of sulfide removal was again elemental-S, which was scarcely released into the liquid, however. Sulfate reduction and sulfur reduction were observed when the light supply was interrupted and were inferred to be occurring within the irradiated biofilm. A preexisting conceptual model of the biofilm was augmented with both of these reductive processes, and this augmented model was shown to account for most of the observed effects of VFA dosing. The implications of these findings for the practicality of the technology are considered. (C) 2004 Wiley Periodicals, Inc.

Some twisted results

The Drinfeld twist for the opposite quasi-Hopf algebra, H-COP, is determined and is shown to be related to the (second) Drinfeld twist on a quasi-Hopf algebra. The twisted form of the Drinfeld twist is investigated. In the quasi-triangular case, it is shown that the Drinfeld u-operator arises from the equivalence of H-COP to the quasi-Hopf algebra induced by twisting H with the R-matrix. The Altschuler-Coste u-operator arises in a similar way and is shown to be closely related to the Drinfeld u-operator. The quasi-cocycle condition is introduced and is shown to play a central role in the uniqueness of twisted structures on quasi-Hopf algebras. A generalization of the dynamical quantum Yang-Baxter equation, called the quasi-dynamical quantum Yang-Baxter equation, is introduced.

A First Order Predicate Logic Formulation of the 3D Reconstruction Problem and its Solution Space

This paper defines the 3D reconstruction problem as the process of reconstructing a 3D scene from numerous 2D visual images of that scene. It is well known that this problem is ill-posed, and numerous constraints and assumptions are used in 3D reconstruction algorithms in order to reduce the solution space. Unfortunately, most constraints only work in a certain range of situations and often constraints are built into the most fundamental methods (e.g. Area Based Matching assumes that all the pixels in the window belong to the same object). This paper presents a novel formulation of the 3D reconstruction problem, using a voxel framework and first order logic equations, which does not contain any additional constraints or assumptions. Solving this formulation for a set of input images gives all the possible solutions for that set, rather than picking a solution that is deemed most likely. Using this formulation, this paper studies the problem of uniqueness in 3D reconstruction and how the solution space changes for different configurations of input images. It is found that it is not possible to guarantee a unique solution, no matter how many images are taken of the scene, their orientation or even how much color variation is in the scene itself. Results of using the formulation to reconstruct a few small voxel spaces are also presented. They show that the number of solutions is extremely large for even very small voxel spaces (5 x 5 voxel space gives 10 to 10(7) solutions). This shows the need for constraints to reduce the solution space to a reasonable size. Finally, it is noted that because of the discrete nature of the formulation, the solution space size can be easily calculated, making the formulation a useful tool to numerically evaluate the usefulness of any constraints that are added.

Professional doctoral training in psychology: International comparison and commentary

The level of training required for the practice of professional psychology varies across countries, and usually evolves from a combination of input from local and national regulatory bodies, legislative requirements, academic institutions and relevant professional bodies. Here we explore the North American and Australian historical developments and future directions in levels of training required and aspired to for professional psychologists, along with a brief comparison to training for psychologists in Central and South America, Europe and Asia. The recent proliferation of professional doctorate degrees in Australian universities has added another layer to the suite of available qualifications for professional psychologists and to some degree reflects international trends in the profession. The important role of professional organisations in establishing the educational requirements for entry into professional practice is highlighted.

Off-line signature verification and forgery detection using fuzzy modeling

Automatic signature verification is a well-established and an active area of research with numerous applications such as bank check verification, ATM access, etc. This paper proposes a novel approach to the problem of automatic off-line signature verification and forgery detection. The proposed approach is based on fuzzy modeling that employs the Takagi-Sugeno (TS) model. Signature verification and forgery detection are carried out using angle features extracted from box approach. Each feature corresponds to a fuzzy set. The features are fuzzified by an exponential membership function involved in the TS model, which is modified to include structural parameters. The structural parameters are devised to take account of possible variations due to handwriting styles and to reflect moods. The membership functions constitute weights in the TS model. The optimization of the output of the TS model with respect to the structural parameters yields the solution for the parameters. We have also derived two TS models by considering a rule for each input feature in the first formulation (Multiple rules) and by considering a single rule for all input features in the second formulation. In this work, we have found that TS model with multiple rules is better than TS model with single rule for detecting three types of forgeries; random, skilled and unskilled from a large database of sample signatures in addition to verifying genuine signatures. We have also devised three approaches, viz., an innovative approach and two intuitive approaches using the TS model with multiple rules for improved performance. (C) 2004 Pattern Recognition Society. Published by Elsevier Ltd. All rights reserved.