Inequalities for zeros of associated polynomials and derivatives of orthogonal polynomials

It is well known and easy to see that the zeros of both the associated polynomial and the derivative of an orthogonal polynomial p(n)(x) interlace with the zeros of p(n)(x) itself. The natural question of how these zeros interlace is under discussion. We give a sufficient condition for the mutual location of kth, 1 less than or equal to k less than or equal to n - 1, zeros of the associated polynomial and the derivative of an orthogonal polynomial in terms of inequalities for the corresponding Cotes numbers. Applications to the zeros of the associated polynomials and the derivatives of the classical orthogonal polynomials are provided. Various inequalities for zeros of higher order associated polynomials and higher order derivatives of orthogonal polynomials are proved. The results involve both classical and discrete orthogonal polynomials, where, in the discrete case, the differential operator is substituted by the difference operator. (C) 2001 IMACS. Published by Elsevier B.V. B.V. All rights reserved.

Strategies for comparing decimal numbers with the same whole-number part

The strategies employed by 130 Grade 5 Brisbane students in comparing decimal numbers which have the same whole-number part were compared with those identified in similar studies conducted in the USA, France and Israel. Three new strategies were identified. Similar to USA results, the most common comparison errors stemmed from the incorrect whole-number strategy in which length is confused with size. The findings of this present study tend to support Resnick et al.’s (1989) hypothesis that the introduction of decimal-fraction recording before common-fraction recording seems to promote better comparison of decimal numbers.

Isaac's Numbers

Short story published in the Queensland University of Technology Student Anthology, Isaac’s Numbers: New Writing from QUT, 2008.

Electron interaction with gel dosimeters : effective atomic numbers for collisional, radiative and total interaction processes

The effective atomic number is widely employed in radiation studies, particularly for the characterisation of interaction processes in dosimeters, biological tissues and substitute materials. Gel dosimeters are unique in that they comprise both the phantom and dosimeter material. In this work, effective atomic numbers for total and partial electron interaction processes have been calculated for the first time for a Fricke gel dosimeter, five hypoxic and nine normoxic polymer gel dosimeters. A range of biological materials are also presented for comparison. The spectrum of energies studied spans 10 keV to 100 MeV, over which the effective atomic number varies by 30 %. The effective atomic numbers of gels match those of soft tissue closely over the full energy range studied; greater disparities exist at higher energies but are typically within 4 %.

Least-squares congealing for large numbers of images

In this paper we pursue the task of aligning an ensemble of images in an unsupervised manner. This task has been commonly referred to as “congealing” in literature. A form of congealing, using a least-squares criteria, has been recently demonstrated to have desirable properties over conventional congealing. Least-squares congealing can be viewed as an extension of the Lucas & Kanade (LK)image alignment algorithm. It is well understood that the alignment performance for the LK algorithm, when aligning a single image with another, is theoretically and empirically equivalent for additive and compositional warps. In this paper we: (i) demonstrate that this equivalence does not hold for the extended case of congealing, (ii) characterize the inherent drawbacks associated with least-squares congealing when dealing with large numbers of images, and (iii) propose a novel method for circumventing these limitations through the application of an inverse-compositional strategy that maintains the attractive properties of the original method while being able to handle very large numbers of images.

Dark numbers: challenges in measuring human trafficking

Over the last decade nations around the world have renewed their efforts to address the problem of human trafficking, following the introduction of the United Nations Protocol to Prevent, Suppress and Punish Trafficking in Persons, Especially Women and Children. In Australia and the United States, legislators sought to quantify and characterise the human trafficking phenomenon, seeking to answer the question — how large is the problem of trafficking? This article explores the attempts of legislators in Australia and the United States to determine how many victims are trafficked into their countries, highlighting the significant uncertainty that still surrounds data on human trafficking. The challenges researchers face in measuring human trafficking are also explored. These challenges include disputes over the definition of a trafficking victim, the limitations of research using sampling to measure the trafficked population, and the mischaracterisation of the trafficking problem as a result of politicisation of the trafficking debate and a focus on trafficking for sexual exploitation versus other forms of labour. This article argues that in the absence of reliable data on trafficking, policy is often informed by misleading or false information.

On the oscillatory behavior of transient Rayleigh Benard convection of air for 2D channel flow at moderate Rayleigh numbers

Unsteady numerical simulation of Rayleigh Benard convection heat transfer from a 2D channel is performed. The oscillatory behavior is attributed to recirculation of ascending and descending flows towards the core of the channel producing organized rolled motions. Variation of the parameters such as Reynolds number, channel outlet flow area and inclination of the channel are considered. Increasing Reynolds number (for a fixed Rayleigh number), delays the generation of vortices. The reduction in the outflow area leads to the later and the less vortex generation. As the time progresses, more vortices are generated, but the reinforced mean velocity does not let the eddies to enter the core of the channel. Therefore, they attach to the wall and reduce the heat transfer area. The inclination of the channel (both positive and negative) induces the generated vortices to get closer to each other and make an enlarged vortex.

Quantitative studies of lower motor neuron degeneration in amyotrophic lateral sclerosis : Evidence for exponential decay of motor unit numbers and greatest rate of loss at the site of onset

Objective: To use our Bayesian method of motor unit number estimation (MUNE) to evaluate lower motor neuron degeneration in ALS. Methods: In subjects with ALS we performed serial MUNE studies. We examined the repeatability of the test and then determined whether the loss of MUs was fitted by an exponential or Weibull distribution. Results: The decline in motor unit (MU) numbers was well-fitted by an exponential decay curve. We calculated the half life of MUs in the abductor digiti minimi (ADM), abductor pollicis brevis (APB) and/or extensor digitorum brevis (EDB) muscles. The mean half life of the MUs of ADM muscle was greater than those of the APB or EDB muscles. The half-life of MUs was less in the ADM muscle of subjects with upper limb than in those with lower limb onset. Conclusions: The rate of loss of lower motor neurons in ALS is exponential, the motor units of the APB decay more quickly than those of the ADM muscle and the rate of loss of motor units is greater at the site of onset of disease. Significance: This shows that the Bayesian MUNE method is useful in following the course and exploring the clinical features of ALS. 2012 International Federation of Clinical Neurophysiology.

More is not necessarily better. A biomechanical study on distal screw numbers in volar locking distal radius plates

INTRODUCTION: Currently available volar locking plates for the treatment of distal radius fractures incorporate at least two distal screw rows for fixation of the metaphyseal fragment and have a variable-angle locking mechanism which allows placement of the screws in various directions There is, however no evidence that these plates translate into better outcomes or have superior biomechanical properties to first generation plates, which had a single distal screw row and fixed-angle locking. The aim of our biomechanical study was to compare fixed-angle single-row plates with variable-angle multi-row plates to clarify the optimal number of locking screws. MATERIALS AND METHODS: Five different plate-screw combinations of three different manufacturers were tested, each group consisting of five synthetic fourth generation distal radius bones. An AO type C2 fracture was created and the fractures were plated according to each manufacturer's recommendations. The specimens then underwent cyclic and load-to-failure testing. An optical motion analysis system was used to detect displacement of fragments. RESULTS: No significant differences were detected after cyclic loading as well as after load-to-failure testing, neither in regard to axial deformation, implant rigidity or maximum displacement. The fixed-angle single-row plate showed the highest pre-test rigidity, least increase in post-testing rigidity and highest load-to-failure rigidity and least radial shortening. The radial shortening of plates with two distal screw rows was 3.1 and 4.3 times higher, respectively, than that of the fixed-angle single-row plate. CONCLUSION: The results of our study indicate that two distal screw rows do not add to construct rigidity and resistance against loss of reduction. Well conducted clinical studies based on the findings of biomechanical studies are necessary to determine the optimal number of screws necessary to achieve reproducibly good results in the treatment of distal radius fractures.

The magic of numbers and the amazing disappearing act : the politics of counting youth homelessness

No-one wants to see young people who are no longer able to stay at home with their parents living in situations that are neither stable nor safe. Most Australians also appreciate that youth homelessness is typically a result of factors beyond the control of young people like poverty, lack of affordable housing, parental divorce or separation, family conflict and violence, sexual abuse, or mental health problems.1 Since the Burdekin Report of 1989 first put the issue on the national agenda, youth homelessness has been a point of some political sensitivity as the numbers of young homeless stayed stubbornly high through the 1990s and into the 2000s.