On the intersection problem for 1-factorizations and near 1-factorizations of K-v

The number of 1-factors (near 1-factors) that mu 1-factorizations (near 1-factorizations) of the complete graph K-v, v even (v odd), can have in common, is studied. The problem is completely settled for mu = 2 and mu = 3.

On the Oberwolfach problem with two similar length cycles

For all in greater than or equal to 3, the Oberwolfach problem is solved for the case where the 2-factors consist of two cycles of lengths in and m + 1, and for the case where the 2-factors consist of two cycles of lengths m and m + 2.

The increasing problem of hepatitis C virus infection

The widespread incidence of hepatitis C (HCV) infection throughout the community is of concern. Although many of those infected will not suffer significantly from their infection, up to one-third will have liver disease, fatigue and oral health problems. General dental practitioners need to be aware of the precautions necessary in treating people with severe liver disease. This paper discusses the issues associated with treating patients who have HCV infection including the importance of preventive programs to reduce dental pathology and maximise oral health.

Hemiplegic shoulder pain: defining the problem and its management

Purpose: Hemiplegic shoulder pain can affect up to 70% of stroke patients and can have an adverse impact on rehabilitation outcomes. This article aims to review the literature on the suggested causes of hemiplegic shoulder pain and the therapeutic techniques that can be used to prevent or treat it. On the basis of this review, the components of an optimal management programme for hemiplegic shoulder pain are explored. Method: English language articles in the CINAHL and MEDLINE databases between 1990 and 2000 were reviewed. These were supplemented by citation tracking and manual searches. Results: A management programme for hemiplegic shoulder pain could comprise the following components: provision of an external support for the affected upper limb when the patient is seated, careful positioning in bed, daily static positional stretches, motor retraining and strapping of the scapula to maintain postural tone and symmetry. Conclusions: Research is required to evaluate the effectiveness of the components of the proposed management programme for the prevention and treatment of hemiplegic shoulder pain and to determine in what combination they achieve the best outcomes.

Critical cyber pedagogy: Doing multiliteracies in the Singapore classrooms

The Ministry of Education in Singapore has embarked on the ambitious project of introducing IT in schools. The IT Masterplan, budgeted at a cost of $2 billion, aims to wire up all schools by the year 2002. While the well-funded IT Masterplan is seeing the project in its final phase of implementation, this paper argues for a "critical cyber pedagogy" along with the acquisition of the functional and operational skills of technology. Drawing on theories of critical multiliteracies (Burbules & Callister, 2000; Luke, 2000b; New London Group, 1996), this paper explores and suggests how an instructional design of two classroom activities can be utilized as new forms of cyber and technoliteracies. Through the critical evaluation of websites and hypertext construction, students will be equipped with a new literacy that extends reading and writing by incorporating new blended forms of hybrid textualities. This technology-assisted pedagogy can achieve the desired outcome of self-directed learning, teamwork, critical thinking and problem solving strategies necessary for a knowledge-based society.

Analysis of flexural waves excited by rectangular contact type transducers

In this paper, an attempt was made to investigate a fundamental problem related to the flexural waves excited by rectangular transducers. Due to the disadvantages of the Green's function approach for solving this problem, a direct and effective method is proposed using a multiple integral transform method and contour integration technique. The explicit frequency domain solutions obtained from this newly developed method are convenient for understanding transducer behavior and theoretical optimization and experimental calibration of rectangular transducers. The time domain solutions can then be easily obtained by using the fast Fourier transform technique. (C) 2001 Elsevier Science B.V. All rights reserved.

Pharmacokinetic software for the health sciences - Choosing the right package for teaching purposes

Computer assisted learning has an important role in the teaching of pharmacokinetics to health sciences students because it transfers the emphasis from the purely mathematical domain to an 'experiential' domain in which graphical and symbolic representations of actions and their consequences form the major focus for learning. Basic pharmacokinetic concepts can be taught by experimenting with the interplay between dose and dosage interval with drug absorption (e.g. absorption rate, bioavailability), drug distribution (e.g. volume of distribution, protein binding) and drug elimination (e.g. clearance) on drug concentrations using library ('canned') pharmacokinetic models. Such 'what if' approaches are found in calculator-simulators such as PharmaCalc, Practical Pharmacokinetics and PK Solutions. Others such as SAAM II, ModelMaker, and Stella represent the 'systems dynamics' genre, which requires the user to conceptualise a problem and formulate the model on-screen using symbols, icons, and directional arrows. The choice of software should be determined by the aims of the subject/course, the experience and background of the students in pharmacokinetics, and institutional factors including price and networking capabilities of the package(s). Enhanced learning may result if the computer teaching of pharmacokinetics is supported by tutorials, especially where the techniques are applied to solving problems in which the link with healthcare practices is clearly established.

Lanczos subspace filter diagonalization: Homogeneous recursive filtering and a low-storage method for the calculation of matrix elements

We develop a new iterative filter diagonalization (FD) scheme based on Lanczos subspaces and demonstrate its application to the calculation of bound-state and resonance eigenvalues. The new scheme combines the Lanczos three-term vector recursion for the generation of a tridiagonal representation of the Hamiltonian with a three-term scalar recursion to generate filtered states within the Lanczos representation. Eigenstates in the energy windows of interest can then be obtained by solving a small generalized eigenvalue problem in the subspace spanned by the filtered states. The scalar filtering recursion is based on the homogeneous eigenvalue equation of the tridiagonal representation of the Hamiltonian, and is simpler and more efficient than our previous quasi-minimum-residual filter diagonalization (QMRFD) scheme (H. G. Yu and S. C. Smith, Chem. Phys. Lett., 1998, 283, 69), which was based on solving for the action of the Green operator via an inhomogeneous equation. A low-storage method for the construction of Hamiltonian and overlap matrix elements in the filtered-basis representation is devised, in which contributions to the matrix elements are computed simultaneously as the recursion proceeds, allowing coefficients of the filtered states to be discarded once their contribution has been evaluated. Application to the HO2 system shows that the new scheme is highly efficient and can generate eigenvalues with the same numerical accuracy as the basic Lanczos algorithm.

Application of Petrov-Galerkin methods to transient boundary value problems in chemical engineering: adsorption with steep gradients in bidisperse solids

Petrov-Galerkin methods are known to be versatile techniques for the solution of a wide variety of convection-dispersion transport problems, including those involving steep gradients. but have hitherto received little attention by chemical engineers. We illustrate the technique by means of the well-known problem of simultaneous diffusion and adsorption in a spherical sorbent pellet comprised of spherical, non-overlapping microparticles of uniform size and investigate the uptake dynamics. Solutions to adsorption problems exhibit steep gradients when macropore diffusion controls or micropore diffusion controls, and the application of classical numerical methods to such problems can present difficulties. In this paper, a semi-discrete Petrov-Galerkin finite element method for numerically solving adsorption problems with steep gradients in bidisperse solids is presented. The numerical solution was found to match the analytical solution when the adsorption isotherm is linear and the diffusivities are constant. Computed results for the Langmuir isotherm and non-constant diffusivity in microparticle are numerically evaluated for comparison with results of a fitted-mesh collocation method, which was proposed by Liu and Bhatia (Comput. Chem. Engng. 23 (1999) 933-943). The new method is simple, highly efficient, and well-suited to a variety of adsorption and desorption problems involving steep gradients. (C) 2001 Elsevier Science Ltd. All rights reserved.

Solution techniques for transport problems involving steep concentration gradients: application to noncatalytic fluid solid reactions

Some efficient solution techniques for solving models of noncatalytic gas-solid and fluid-solid reactions are presented. These models include those with non-constant diffusivities for which the formulation reduces to that of a convection-diffusion problem. A singular perturbation problem results for such models in the presence of a large Thiele modulus, for which the classical numerical methods can present difficulties. For the convection-diffusion like case, the time-dependent partial differential equations are transformed by a semi-discrete Petrov-Galerkin finite element method into a system of ordinary differential equations of the initial-value type that can be readily solved. In the presence of a constant diffusivity, in slab geometry the convection-like terms are absent, and the combination of a fitted mesh finite difference method with a predictor-corrector method is used to solve the problem. Both the methods are found to converge, and general reaction rate forms can be treated. These methods are simple and highly efficient for arbitrary particle geometry and parameters, including a large Thiele modulus. (C) 2001 Elsevier Science Ltd. All rights reserved.