Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.

Evaluation of cyclooxygenase 2 inhibitor use in patients admitted to a large teaching hospital

Background: The heavy usage of coxibs in Australia far outstrips the predicted usage that was based on the treatment of patients with risk factors for upper gastro-intestinal adverse events from conventional anti--inflammatory agents. This raises questions regarding the appropriateness of prescribing. Aims: To determine: (i) the relationship between prescriptions for cyclooxygenase 2 (COX-2) inhibitors and objective evidence of inflammatory arthritis, (ii) prior experience with paracetamol and/or conventional non-steroidal anti-inflammatory drugs (NSAIDs), and (iii) contraindications to the use of NSAIDs. Methods: Drug utilization evaluation and rheumato-logical assessment was conducted on 70 consecutive patients admitted on COX-2 inhibitors to a 480-bed metropolitan hospital. The main outcome measures were: the indication for COX-2 inhibitor; objective -evidence of inflammatory arthritis; previous trial of -paracetamol or conventional NSAIDs; and patient -satisfaction. Results: Only 11 patients (16%) had symptoms or signs of an inflammatory arthropathy, and met Pharmaceut-ical Benefits Schedule criteria for prescribing a COX-2 inhibitor. Fifty-nine patients (84%) had chronic osteo-arthritis, degenerative spinal disease, injury or malignancy, without overt active inflammation. Fourteen patients (20%) had trialled regular paracetamol prior to using any NSAID treatment. Conventional NSAIDs had been previously used by 51 patients (73%). Eleven patients (16%) reported previous adverse gastrointestinal effects from conventional NSAIDs. On the basis of significant renal impairment (creatinine clearance 5/10). Conclusions: Drug utilization data indicate that COX-2 inhibitors are frequently used first line for degenerative osteoarthritis in the absence of overt inflammation, without prior adequate trial of paracetamol and with disregard for the cautions and contraindications of these agents. These findings may explain the unprecedented Pharmaceutical Benefits Schedule expenditure on COX-2 inhibitors in Australia.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Lectures and other types of teaching

A questionnaire on lectures was completed by 351 students (84% response) and 35 staff (76% response) from all five years of the veterinary course at the University of Queensland. Staff and students in all five years offered limited support for a reduction in the number of lectures in the course and the majority supported a reduction in the number of lectures in the clinical years. Students in the clinical years only and appropriate staff agreed that the number of lectures in fifth year should be reduced but were divided as to whether lectures in fifth year should be abolished. There was limited support for replacement of some lectures by computer assisted learning (CAL) programs, but strong support for replacement of some lectures by subject-based problem based learning (PBL) and strong support for more self-directed learning by students. Staff and students strongly supported the inclusion of more clinical problem solving in lectures in the clinical years and wanted these lectures to be more interactive. There was little support for lectures in the clinical years to be of the same type as in the preclinical years.

Dynamic stability of laminated FGM plates based on higher-order shear deformation theory

This paper conducts a dynamic stability analysis of symmetrically laminated FGM rectangular plates with general out-of-plane supporting conditions, subjected to a uniaxial periodic in-plane load and undergoing uniform temperature change. Theoretical formulations are based on Reddy's third-order shear deformation plate theory, and account for the temperature dependence of material properties. A semi-analytical Galerkin-differential quadrature approach is employed to convert the governing equations into a linear system of Mathieu-Hill equations from which the boundary points on the unstable regions are determined by Bolotin's method. Free vibration and bifurcation buckling are also discussed as subset problems. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with FGM layers made of silicon nitride and stainless steel. The influences of various parameters such as material composition, layer thickness ratio, temperature change, static load level, boundary constraints on the dynamic stability, buckling and vibration frequencies are examined in detail through parametric studies.

Historical and dialectical perspectives on the teaching of Aboriginal and Torres Strait Islander musics in the Australian education system

Indigenous studies (also referred to as Aboriginal and Torres Strait Islander studies) has a double identity in the Australian education system, consisting of the education of Indigenous students and education of all students about Aboriginal and Torres Strait Islander cultures and histories. Through explanations of the history of the inclusion of Aboriginal and Torres Strait Islander musics in Australian music education, this article critiques ways in which these musics have been positioned in relation to a number of agendas. These include definitions of Aboriginal and Torres Strait Islander musics as types of Australian music, as ethnomusicological objects, as examples of postcolonial discourse, and as empowerment for Indigenous students. The site of discussion is the work of the Australian Society for Music Education, as representative of trends in Australian school-based music education, and the Centre for Aboriginal Studies in Music at the University of Adelaide, as an example of a tertiary music program for Indigenous students.

A review of drainage and spontaneous rupture in free standing thin films with tangentially immobile interfaces

A review of spontaneous rupture in thin films with tangentially immobile interfaces is presented that emphasizes the theoretical developments of film drainage and corrugation growth through the linearization of lubrication theory in a cylindrical geometry. Spontaneous rupture occurs when corrugations from adjacent interfaces become unstable and grow to a critical thickness. A corrugated interface is composed of a number of waveforms and each waveform becomes unstable at a unique transition thickness. The onset of instability occurs at the maximum transition thickness, and it is shown that only upper and lower bounds of this thickness can be predicted from linear stability analysis. The upper bound is equivalent to the Freakel criterion and is obtained from the zeroth order approximation of the H-3 term in the evolution equation. This criterion is determined solely by the film radius, interfacial tension and Hamaker constant. The lower bound is obtained from the first order approximation of the H-3 term in the evolution equation and is dependent on the film thinning velocity A semi-empirical equation, referred to as the MTR equation, is obtained by combining the drainage theory of Manev et al. [J. Dispersion Sci. Technol., 18 (1997) 769] and the experimental measurements of Radoev et al. [J. Colloid Interface Sci. 95 (1983) 254] and is shown to provide accurate predictions of film thinning velocity near the critical thickness of rupture. The MTR equation permits the prediction of the lower bound of the maximum transition thickness based entirely on film radius, Plateau border radius, interfacial tension, temperature and Hamaker constant. The MTR equation extrapolates to Reynolds equation under conditions when the Plateau border pressure is small, which provides a lower bound for the maximum transition thickness that is equivalent to the criterion of Gumerman and Homsy [Chem. Eng. Commun. 2 (1975) 27]. The relative accuracy of either bound is thought to be dependent on the amplitude of the hydrodynamic corrugations, and a semiempirical correlation is also obtained that permits the amplitude to be calculated as a function of the upper and lower bound of the maximum transition thickness. The relationship between the evolving theoretical developments is demonstrated by three film thickness master curves, which reduce to simple analytical expressions under limiting conditions when the drainage pressure drop is controlled by either the Plateau border capillary pressure or the van der Waals disjoining pressure. The master curves simplify solution of the various theoretical predictions enormously over the entire range of the linear approximation. Finally, it is shown that when the Frenkel criterion is used to assess film stability, recent studies reach conclusions that are contrary to the relevance of spontaneous rupture as a cell-opening mechanism in foams. (C) 2003 Elsevier Science B.V. All rights reserved.