On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

Density of Polynomials in the L^2 Space on the Real and the Imaginary Axes and in a Sobolev Space

2000 Mathematics Subject Classification: 41A10, 30E10, 41A65.

Influence of the cutting edge micro-geometry of PCBN tools on the flank wear in orthogonal quenched and tempered turning M2 steel

Quenched and tempered high-speed steels obtained by powder metallurgy are commonly used in automotive components, such as valve seats of combustion engines. In order to machine these components, tools with high wear resistance and appropriate cutting edge geometry are required. This work aims to investigate the influence of the edge preparation of polycrystalline cubic boron nitride (PCBN) tools on the wear behavior in the orthogonal longitudinal turning of quenched and tempered M2 high-speed steels obtained by powder metallurgy. For this research, PCBN tools with high and low-CBN content have been used. Two different cutting edge geometries with a honed radius were tested: with a ground land (S shape) and without it (E shape). Also, the cutting speed was varied from 100 to 220 m/min. A rigid CNC lathe was used. The results showed that the high-CBN, E-shaped tool presented the longest life for a cutting speed of 100 m/min. High-CBN tools with a ground land and honed edge radius (S shaped) showed edge damage and lower values of the tool’s life. Low-CBN, S-shaped tools showed similar results, but with an inferior performance when compared with tools with high CBN content in both forms of edge preparation.

Evaluation of contextual influences on the medication administration practice of paediatric nurses

Aim. This paper is a report of a study conducted to explore the impact of preidentified contextual themes (related to work environment and socialization) on nursing medication practice. Background. Medication administration is a complex aspect of paediatric nursing and an important component of day-to-day nursing practice. Many attempts are being made to improve patient safety, but many errors remain. Identifying and understanding factors that influence medication administration errors are of utmost importance. Method. A cross-sectional survey was conducted with a sample of 278 paediatric nurses from the emergency department, intensive care unit and medical and surgical wards of an Australian tertiary paediatric hospital in 2004. The response rate was 67%. Result. Contextual influences were important in determining how closely medication policy was followed. Completed questionnaires were returned by 185 nurses (67%). Younger nurses aged <34 years thought that their medication administration practice could be influenced by the person with whom they checked the drugs (P = 0·001), and that there were daily circumstances when it was acceptable not to adhere strictly to medication policy (P < 0·001), including choosing between following policy and acting in the best interests of the child (P = 0·002). Senior nurses agreed that senior staff dictate acceptable levels of medication policy adherence through role modelling (P = 0·01). Less experienced nurses reported greater confidence with computer literacy (P < 0·001). Conclusions. Organizations need to employ multidisciplinary education programmes to promote universal understanding of, and adherence to, medication policies. Skill mix should be closely monitored to ensure adequate support for new and junior staff.

The impact of managers' characteristics on the use of public relations strategy : an exploratory study in Queensland schools

While previous positive and normative studies have focused on the role public relations should play in organisations and the need for management in all organisations to attend to public relations (Cutlip et al., 2006), there has been little discussion in the public relations literature on why or how managers choose to enact public relations strategies for their organisations. If the discipline of public relations is to cement itself as a management function, then researchers must gain a better understanding of managers themselves given that they are the ones who decide if and how public relations strategies should be employed in the organisation. This study has sought to explore evidence of a relationship between management characteristics and their impact on decisions managers make when choosing which public relations strategies to adopt in response to changes in the organisation’s operating environment. This exploratory research study has been conducted within a specific context of schools in Queensland, Australia. Queensland schools have been facing a number of changes within their operating environment due to changes in Federal funding models in Australia’s education system. This study used an exploratory, qualitative approach to understand the management characteristics demonstrated by managers in schools and how these have impacted on the selection of public relations strategies for responding to their changing and increasingly competitive environment. The unit of analysis for this research study was principals in State (government) schools and in non-government schools. Ten principals were interviewed from four different types of schools in Queensland – the more traditional, elite, private schools (GPS Schools); other Independent Schools; Catholic Schools; and State (or public) schools. These interviews were analysed for quantitative comparisons of the managers’ characteristics across the different schools (in terms of the number of principals in each age bracket, those holding postgraduate qualifications, years of experience etc.); and for qualitative data to provide a greater sense of their understanding of public relations. The 10 schools were selected within a geographic area from Brisbane’s inner city to its outer western suburbs to include an element of competition amongst those managers being interviewed. A detailed review of government, school and other public documents was also conducted to gain an insight into the environment in which principals made decisions about public relations strategy to respond to increasing competition. This study found support for the literature on the relationship between management characteristics and strategy. However, there was also variation in findings warranting further investigation of the literature on the relationship between management characteristics and strategy in a school setting. Key relationships found in this study were between: management characteristics themselves; age and the use of public relations strategies; and gender and the use of public relations strategies. There was also evidence of support for the literature linking the impact that the combination of managers’ age, education and experience had on the use of public relations strategies. While this study was exploratory in nature, it did reveal a number of areas that require further investigation to gain a deeper understanding of how and why managers choose public relations strategies as a response to changes in their operating environment. It also provided a different framework to gain a better understanding of managers’ understanding and support of public relations in schools, which, in conjunction with an analysis of their management characteristics, will hopefully allow public relations scholars and practitioners alike gain an understanding of how and why managers use public relations strategies.

The effect of red blood cell orientation on the electrical impedance of pulsatile blood with implications for impedance cardiography

Impedance cardiography is an application of bioimpedance analysis primarily used in a research setting to determine cardiac output. It is a non invasive technique that measures the change in the impedance of the thorax which is attributed to the ejection of a volume of blood from the heart. The cardiac output is calculated from the measured impedance using the parallel conductor theory and a constant value for the resistivity of blood. However, the resistivity of blood has been shown to be velocity dependent due to changes in the orientation of red blood cells induced by changing shear forces during flow. The overall goal of this thesis was to study the effect that flow deviations have on the electrical impedance of blood, both experimentally and theoretically, and to apply the results to a clinical setting. The resistivity of stationary blood is isotropic as the red blood cells are randomly orientated due to Brownian motion. In the case of blood flowing through rigid tubes, the resistivity is anisotropic due to the biconcave discoidal shape and orientation of the cells. The generation of shear forces across the width of the tube during flow causes the cells to align with the minimal cross sectional area facing the direction of flow. This is in order to minimise the shear stress experienced by the cells. This in turn results in a larger cross sectional area of plasma and a reduction in the resistivity of the blood as the flow increases. Understanding the contribution of this effect on the thoracic impedance change is a vital step in achieving clinical acceptance of impedance cardiography. Published literature investigates the resistivity variations for constant blood flow. In this case, the shear forces are constant and the impedance remains constant during flow at a magnitude which is less than that for stationary blood. The research presented in this thesis, however, investigates the variations in resistivity of blood during pulsataile flow through rigid tubes and the relationship between impedance, velocity and acceleration. Using rigid tubes isolates the impedance change to variations associated with changes in cell orientation only. The implications of red blood cell orientation changes for clinical impedance cardiography were also explored. This was achieved through measurement and analysis of the experimental impedance of pulsatile blood flowing through rigid tubes in a mock circulatory system. A novel theoretical model including cell orientation dynamics was developed for the impedance of pulsatile blood through rigid tubes. The impedance of flowing blood was theoretically calculated using analytical methods for flow through straight tubes and the numerical Lattice Boltzmann method for flow through complex geometries such as aortic valve stenosis. The result of the analytical theoretical model was compared to the experimental impedance measurements through rigid tubes. The impedance calculated for flow through a stenosis using the Lattice Boltzmann method provides results for comparison with impedance cardiography measurements collected as part of a pilot clinical trial to assess the suitability of using bioimpedance techniques to assess the presence of aortic stenosis. The experimental and theoretical impedance of blood was shown to inversely follow the blood velocity during pulsatile flow with a correlation of -0.72 and -0.74 respectively. The results for both the experimental and theoretical investigations demonstrate that the acceleration of the blood is an important factor in determining the impedance, in addition to the velocity. During acceleration, the relationship between impedance and velocity is linear (r2 = 0.98, experimental and r2 = 0.94, theoretical). The relationship between the impedance and velocity during the deceleration phase is characterised by a time decay constant, ô , ranging from 10 to 50 s. The high level of agreement between the experimental and theoretically modelled impedance demonstrates the accuracy of the model developed here. An increase in the haematocrit of the blood resulted in an increase in the magnitude of the impedance change due to changes in the orientation of red blood cells. The time decay constant was shown to decrease linearly with the haematocrit for both experimental and theoretical results, although the slope of this decrease was larger in the experimental case. The radius of the tube influences the experimental and theoretical impedance given the same velocity of flow. However, when the velocity was divided by the radius of the tube (labelled the reduced average velocity) the impedance response was the same for two experimental tubes with equivalent reduced average velocity but with different radii. The temperature of the blood was also shown to affect the impedance with the impedance decreasing as the temperature increased. These results are the first published for the impedance of pulsatile blood. The experimental impedance change measured orthogonal to the direction of flow is in the opposite direction to that measured in the direction of flow. These results indicate that the impedance of blood flowing through rigid cylindrical tubes is axisymmetric along the radius. This has not previously been verified experimentally. Time frequency analysis of the experimental results demonstrated that the measured impedance contains the same frequency components occuring at the same time point in the cycle as the velocity signal contains. This suggests that the impedance contains many of the fluctuations of the velocity signal. Application of a theoretical steady flow model to pulsatile flow presented here has verified that the steady flow model is not adequate in calculating the impedance of pulsatile blood flow. The success of the new theoretical model over the steady flow model demonstrates that the velocity profile is important in determining the impedance of pulsatile blood. The clinical application of the impedance of blood flow through a stenosis was theoretically modelled using the Lattice Boltzman method (LBM) for fluid flow through complex geometeries. The impedance of blood exiting a narrow orifice was calculated for varying degrees of stenosis. Clincial impedance cardiography measurements were also recorded for both aortic valvular stenosis patients (n = 4) and control subjects (n = 4) with structurally normal hearts. This pilot trial was used to corroborate the results of the LBM. Results from both investigations showed that the decay time constant for impedance has potential in the assessment of aortic valve stenosis. In the theoretically modelled case (LBM results), the decay time constant increased with an increase in the degree of stenosis. The clinical results also showed a statistically significant difference in time decay constant between control and test subjects (P = 0.03). The time decay constant calculated for test subjects (ô = 180 - 250 s) is consistently larger than that determined for control subjects (ô = 50 - 130 s). This difference is thought to be due to difference in the orientation response of the cells as blood flows through the stenosis. Such a non-invasive technique using the time decay constant for screening of aortic stenosis provides additional information to that currently given by impedance cardiography techniques and improves the value of the device to practitioners. However, the results still need to be verified in a larger study. While impedance cardiography has not been widely adopted clinically, it is research such as this that will enable future acceptance of the method.

Engaging operations management students by designing the unit with industry focus

Operations management is an area concerned with the production of goods and services ensuring that business operations are efficient in utilizing resource and effective to meet customer requirements. It deals with the design and management of products, processes, services and supply chains and considers the acquisition, development, and effective and efficient utilization of resources. Unlike other engineering subjects, content of these units could be very wide and vast. It is therefore necessary to cover the content that is most related to the contemporary industries. It is also necessary to understand what engineering management skills are critical for engineers working in the contemporary organisations. Most of the operations management books contain traditional Operations Management techniques. For example ‘inventory management’ is an important topic in operations management. All OM books deal with effective method of inventory management. However, new trend in OM is Just in time (JIT) delivery or minimization of inventory. It is therefore important to decide whether to emphasise on keeping inventory (as suggested by most books) or minimization of inventory. Similarly, for OM decisions like forecasting, optimization and linear programming most organisations now a day’s use software. Now it is important for us to determine whether some of these software need to be introduced in tutorial/ lab classes. If so, what software? It is established in the Teaching and Learning literature that there must be a strong alignment between unit objectives, assessment and learning activities to engage students in learning. Literature also established that engaging students is vital for learning. However, engineering units (more specifically Operations management) is quite different from other majors. Only alignment between objectives, assessment and learning activities cannot guarantee student engagement. Unit content must be practical oriented and skills to be developed should be those demanded by the industry. Present active learning research, using a multi-method research approach, redesigned the operations management content based on latest developments in Engineering Management area and the necessity of Australian industries. The redesigned unit has significantly helped better student engagement and better learning. It was found that students are engaged in the learning if they find the contents are helpful in developing skills that are necessary in their practical life.

Investigating the deployment of project management : a new perspective based on the concept of certification

Purpose – The purpose of this paper is to provide a summary description of the doctoral thesis investigating the field of project management (PM) deployment. Researchers will be informed of the current contributions within this topic and of the possible further investigations and researches. The decision makers and practitioners will be aware of a set of tools addressing the PM deployment with new perspectives. Design/methodology/approach – Research undertaken with the thesis is based on quantitative methods using time series statistics (time distance analysis) and comparative and correlation analysis aimed to better define and understand the PM deployment within and between countries or groups. Findings – The results suggest a project management deployment index (PMDI) to objectively measure the PM deployment based on the concept of certification. A proposed framework to empirically benchmark the PM deployment between countries by integrating the PMDI time series with the two dimensional comparative analysis of Sicherl. The correlation analysis within Hoftsede cultural framework shows the impact of the national culture dimensions on the PM deployment. The forecasting model shows a general continual growth trend of the PM deployment, with continual increase in the time distance between the countries. Research limitations/implications – The PM researchers are offered an empirical quantification on which they can construct further investigations and understanding of this phenomenon. The number of possible units that can be studied offers wide possibilities to replicate the thesis work. New researches can be undertaken to investigate further the contribution of other social or economical indicators, or to refine and enrich the definition of the PMDI indicator. Practical implications – These results have important implications on the PM deployment approaches. The PMDI measurements and time series comparisons facilitate considerably the measurement and benchmarking between the units (e.g. countries) and against targets, while the readiness setting of the studied unit (in terms of development and cultural levels) impacts the PM deployment within this country. Originality/value – This paper provides a summary of cutting-edge research work in the studied field of PM deployment and a link to the published works that researchers can use to help them understand the thesis research as well as how it can be extended.

Report on the AIDS Vaccine 2008 Conference

The "AIDS Vaccine 2008" Conference was held in Cape Town, South Africa (October 13 to 16, 2008) and organized, under the aegis of the Global HIV Vaccine Enterprise, by Dr. Lynn Morris (Chair of the Conference) National Institute of Communicable Diseases; Dr. Koleka Mlisana from CAPRISA, University KwaZulu-Natal, Durban, Dr. Glenda Gray from Perinatal HIV Research Unit, University Witwatersrand, Johannesburg and Dr. Carolyn Williamson from Institute of Infectious Diseses. and Molecular Medicine, UCT, Cape Town (Co-Chairs of the Conference). Since the first AIDS Vaccine conference, organized in Paris in 2000, this was the first time it was held outside of the U.S. and Europe, and involved nearly 1,000 participants. Besides three Plenary Sessions with ten state-of-the-art plenary lectures and one Keynote Lecture given by Dr. A.S. Fauci (Director of NIAID, NIH, USA), the Conference was organized in nine oral sessions, four poster discussion groups covering a wide spectrum of scientific information relating to HIV vaccine research and development. Moreover three Symposia, two Special Sessions, one Roundtable as well as two Debates were held, the latter focusing on current controversial topics. The conference opening was memorable for a number of reasons: among these was the presence of South Africa's new Minister of Health, Barbara Hogan who, in her first speech in a major forum as a senior member of the SA Government, affirmed that HIV causes AIDS, and that the search for a vaccine is of paramount importance to SA and the rest of the world. A scientific summary of the Conference is reported in the present article, divided into four major topics: (1) vaccine concepts and design; (2) T-cell immunology and innate immunity; (3) B-cell immunology, neutralizing antibodies and mucosal immunology; and (4) clinical trials. © 2009 Landes Bioscience.

Dry powder inhaler formulations : effect of carrier size on the drug dispersion

Background: The size of the carrier influences drug aerosolization from a dry powder inhaler (DPI) formulation. Lactose particles with irregular shape and rough surface in a variety of sizes are additionally used as carriers; however, contradictory reports exist regarding the effect of carrier size on the dispersion of drug. We examined the influence of the spherical particle size of the biodegradable polylactide-co-glycolide (PLGA) carrier on the aerosolization of a model drug, salbutamol sulphate (SS). Methods: Four different sizes (20-150 µm) of polymer carriers were fabricated using solvent evaporation technique and the dispersion of SS from these carriers was measured by a Twin Stage Impinger (TSI). The size and morphological properties of polymer carriers were determined by laser diffraction and SEM, respectively. Results: The FPF was found to increase from 5.6% to 21.3% with increasing carrier sizeup to150 µm. Conclusions: The aerosolization of drug increased linearly with the size of polymer carriers. For a fixed mass of drug particles in a formulation, the mass of drug particles per unit area of carriers is higher in formulations containing the larger carriers, which leads to an increase in the dispersion of drug due to the increased mechanical forces occurred between the carriers and the device walls.

Effect of aging time and Al substitution on the morphology of aluminous goethite

Goethite and Al-substituted goethite were synthesized from the reaction between ferric nitrate and/or aluminum nitrate and potassium hydroxide. XRF, XRD, TEM with EDS were used to characterize the chemical composition, phase and lattice parameters, and morphology of the synthesized products. The results show that d(020) decreases from 4.953 to 4.949 Å and the b dimension decreases from 9.951 Å to 9.906 Å when the aging time increases from 6 days to 42 days for 9.09 mol% Al-substituted goethite. A sample with 9.09 mol% Al substitution in Al-substituted goethite was prepared by a rapid co-precipitation method. In the sample, 13.45 mol%, 12.31 mol% and 5.85 mol% Al substitution with a crystal size of 163, 131, and 45 nm are observed as shown in the TEM images and EDS. The crystal size of goethite is positively related to the degree of Al substitution according to the TEM images and EDS results. Thus, this methodology is proved to be effective to distinguish the morphology of goethite and Al substituted goethite.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Dry powder inhaler formulations-effect of polymer carrier size on the drug dispersion

Background The size of the carrier influences the aerosolization of drug from a dry powder inhaler (DPI) formulation. Currently, lactose monohydrate particles in a variety of sizes are preferably used in carrier based DPI formulations of various drugs; however, contradictory reports exist regarding the effect of the size of the carrier on the dispersion of drug. In this study we examined the influence of the intrinsic particle size of the polymeric carrier on the aerosolization of a model drug salbutamol sulphate (SS). Methods Four different sizes (20–150 lm) of polymer carriers were fabricated using solvent evaporation technique and the dispersion of SS particles from these carriers was measured by a Twin Stage Impinger (TSI). The size and morphological properties of polymer carriers were by laser diffraction and SEM, respectively. Results The FPF from these carriers was found to be increasing from 5.6% to 21.3% with increasing the carrier size. The FPF was found to be greater (21%) with the highest particle size of the carrier (150 lm). Conclusions The aerosolization of drug was dependent on the size of polymer carriers. The smaller size of the carrier resulted in lower FPF which was increased with increasing the carrier size. For a fixed mass of drug particles in a formulation, the mass of drug particles per unit area of carriers is higher in formulations containing the larger carriers, which leads to an increase in the dispersion of drug due to the increased mechanical forces occurred between the carriers and the device walls.