Constructive development of the solutions of linear equations in introductory ordinary differential equations

The solution of linear ordinary differential equations (ODEs) is commonly taught in first year undergraduate mathematics classrooms, but the understanding of the concept of a solution is not always grasped by students until much later. Recognising what it is to be a solution of a linear ODE and how to postulate such solutions, without resorting to tables of solutions, is an important skill for students to carry with them to advanced studies in mathematics. In this study we describe a teaching and learning strategy that replaces the traditional algorithmic, transmission presentation style for solving ODEs with a constructive, discovery based approach where students employ their existing skills as a framework for constructing the solutions of first and second order linear ODEs. We elaborate on how the strategy was implemented and discuss the resulting impact on a first year undergraduate class. Finally we propose further improvements to the strategy as well as suggesting other topics which could be taught in a similar manner.

The differential effects of organizational antecedents on dimensions of corporate entrepreneurship

This study seeks to further delineate how organizational antecedents differentially influence the three components of corporate entrepreneurship: innovation, venturing or strategic renewal. We argue that structural differentiation may help organizations to maintain multiple and often conflicting demands of entrepreneurial and mainstream activities. Taking a social capital perspective, our study further examines two contingencies in the form of informal integration mechanisms (i.e. connectedness and TMT social integration). Our findings show structural differentiation has a positive effect on all three components of corporate entrepreneurship, yet the effect is moderated by integration mechanisms. Interunit connectedness has a positive moderation effect regarding innovation and venturing, and TMT social integration has a negative moderation effect regarding strategic renewal. This reveals that innovation is influenced by informal integration mechanisms on the organizational level, strategic renewal on top management team level, while venturing is influenced by integration mechanisms on both levels.

Increasing socio-economic inequalities in drug-induced deaths in Australia : 1981-2002

Introduction and Aims: Since the 1990s illicit drug use death rates in Australia have increased markedly. There is a notable gap in knowledge about changing socio-economic inequalities in drug use death rates. Some limited Australian and overseas data point to higher rates of drug death in the lowest socio-economic groups, but the paucity of available studies and their sometimes conflicting findings need to be addressed. Design and Methods: This paper uses data obtained from the Australian Bureau of Statistics (ABS) to examine changes in age-standardised drug-induced mortality rates for Australian males over the period 1981 – 2002. Socio-economic status was categorised as manual or non-manual work status. Results: With the rapid increase in drug-induced mortality rates in the 1990s, there was a parallel increase in socio-economic inequalities in drug-induced deaths. The decline in drug death rates from 2000 onwards was associated with a decline in socio-economic inequalities. By 2002, manual workers had drug death rates well over twice the rate of non-manual workers. Discussion: Three factors are identified which contribute to these socio-economic inequalities in mortality. First, there has been an age shift in deaths evident only for manual workers. Secondly, there has been an increase in availability until 1999 and a relative decline in the cost of the drug, which most often leads to drug death (heroin). Thirdly, there has been a shift to amphetamine use which may lead to significant levels of morbidity, but few deaths. [Najman JM, Toloo G, Williams GM. Increasing socio-economic inequalities in drug-induced deaths in Australia: 1981–2002.

Differential reporting and the effect on loan evaluations : an experimental study

This study utilises a mexed design laboratory experiment to test the impact of differential reporting on one group of external financial report users-lenders. The results indicate that the judgments of bank loan officers' assessment of the ability of a borrower to repay, are not significantly affected by differential reporting (in this case, presentation on non-GAAP financial reports compared to GAAP financial reports). However, bankers request additional information from borrowers when non-GAAP financial reports are presented.

Thermal transition properties of spagehetti measured by Differential Scanning Calorimetry (DSC) and Thermal Mechanical Compression Test (TMCT)

Glass transition temperature of spaghetti sample was measured by thermal and rheological methods as a function of water content.

Simultaneous determination of three synthetic glucocorticoids by differential pulse stripping voltammetry with the aid of chemometrics

A novel voltammetric method for simultaneous determination of the glucocorticoid residues prednisone, prednisolone, and dexamethasone was developed. All three compounds were reduced at a mercury electrode in a Britton-Robinson buffer (pH 3.78), and well-defined voltammetric waves were observed. However, the voltammograms of these three compounds overlapped seriously and showed nonlinear character, and thus, it was difficult to analyze the compounds individually in their mixtures. In this work, two chemometrics methods, principal component regression (PCR) and partial least squares (PLS), were applied to resolve the overlapped voltammograms, and the calibration models were established for simultaneous determination of these compounds. Under the optimum experimental conditions, the limits of detection (LOD) were 5.6, 8.3, and 16.8 µg l-1 for prednisone, prednisolone, and dexamethasone, respectively. The proposed method was also applied for the determination of these glucocorticoid residues in the rabbit plasma and human urine samples with satisfactory results.

A differential kinetic spectrophotometric method for determination of three sulphanilamide artificial sweeteners with the aid of chemometrics

A simple and sensitive spectrophotometric method for the simultaneous determination of acesulfame-K, sodium cyclamate and saccharin sodium sweeteners in foodstuff samples has been researched and developed. This analytical method relies on the different kinetic rates of the analytes in their oxidative reaction with KMnO4 to produce the green manganate product in an alkaline solution. As the kinetic rates of acesulfame-K, sodium cyclamate and saccharin sodium were similar and their kinetic data seriously overlapped, chemometrics methods, such as partial least squares (PLS), principal component regression (PCR) and classical least squares (CLS), were applied to resolve the kinetic data. The results showed that the PLS prediction model performed somewhat better. The proposed method was then applied for the determination of the three sweeteners in foodstuff samples, and the results compared well with those obtained by the reference HPLC method.

Social inequalities and parent involvement in children’s education in the early years of school

Strengthening cooperation between schools and parents is critical to improving learning outcomes for children. The chapter focuses on parental engagement in their children’s education in the early years of school. It considers issues of social and cultural capital as important to whether, or not, parents are involved in their children’s schooling. Analyses of data from a national representative sample of children and their families who participate in Growing up in Australia: The Longitudinal Study of Australian Children are presented. Results indicated that higher family socio-economic position was associated with higher levels of parental involvement and higher expectations about children’s future level of education.

Numerical methods for fractional partial differential equations with Riesz space fractional derivatives

In this paper, we consider the numerical solution of a fractional partial differential equation with Riesz space fractional derivatives (FPDE-RSFD) on a finite domain. Two types of FPDE-RSFD are considered: the Riesz fractional diffusion equation (RFDE) and the Riesz fractional advection–dispersion equation (RFADE). The RFDE is obtained from the standard diffusion equation by replacing the second-order space derivative with the Riesz fractional derivative of order αset membership, variant(1,2]. The RFADE is obtained from the standard advection–dispersion equation by replacing the first-order and second-order space derivatives with the Riesz fractional derivatives of order βset membership, variant(0,1) and of order αset membership, variant(1,2], respectively. Firstly, analytic solutions of both the RFDE and RFADE are derived. Secondly, three numerical methods are provided to deal with the Riesz space fractional derivatives, namely, the L1/L2-approximation method, the standard/shifted Grünwald method, and the matrix transform method (MTM). Thirdly, the RFDE and RFADE are transformed into a system of ordinary differential equations, which is then solved by the method of lines. Finally, numerical results are given, which demonstrate the effectiveness and convergence of the three numerical methods.

Socioeconomic differences in takeaway food consumption and their contribution to inequalities in dietary intakes

Background Takeaway consumption has been increasing and may contribute to socioeconomic inequalities in overweight/obesity and chronic disease. This study examined socioeconomic differences in takeaway consumption patterns, and their contributions to dietary intake inequalities. Method Cross-sectional dietary intake data from adults aged between 25 and 64 years from the Australian National Nutrition Survey (n= 7319, 61% response rate). Twenty-four hour dietary recalls ascertained intakes of takeaway food, nutrients and fruit and vegetables. Education was used as socioeconomic indicator. Data were analysed using logistic regression and general linear models. Results Thirty-two percent (n = 2327) consumed takeaway foods in the 24 hour period. Lower-educated participants were less likely than their higher-educated counterparts to have consumed total takeaway foods (OR 0.64; 95% CI 0.52, 0.80). Of those consuming takeaway foods, the lowest-educated group was more likely to have consumed “less healthy” takeaway choices (OR 2.55; 95% CI 1.73, 3.77), and less likely to have consumed “healthy” choices (OR 0.52; 95% CI 0.36, 0.75). Takeaway foods made a greater contribution to energy, total fat, saturated fat, and fibre intakes among lower than higher-educated groups. Lower likelihood of fruit and vegetable intakes were observed among “less healthy” takeaway consumers, whereas a greater likelihood of their consumption was found among “healthy” takeaway consumers. Conclusions Total and the types of takeaway foods consumed may contribute to socioeconomic inequalities in intakes of energy, total and saturated fats. However, takeaway consumption is unlikely to be a factor contributing to the lower fruit and vegetable intakes among socioeconomically-disadvantaged groups.

Inequalities in cardiovascular disease mortality : the role of behavioural, physiological and social risk factors

Background: While the relationship between socioeconomic disadvantage and cardiovascular disease (CVD) is well established, the role that traditional cardiovascular risk factors play in this association remains unclear. We examined the association between education attainment and CVD mortality and the extent to which behavioural, social and physiological factors explained this relationship. Methods: Adults (n=38 355) aged 40-69 years living in Melbourne, Australia were recruited in 1990-1994. Subjects with baseline CVD risk factor data ascertained through questionnaire and physical measurement were followed for an average of 9.4 years with CVD deaths verified by review of medical records and autopsy reports. Results: CVD mortality was higher for those with primary education only compared to those who had completed tertiary education, with a hazard ratio (HR) of 1.66 (95% confidence interval [CI] 1.11-2.49) after adjustment for age, country of birth and gender. Those from the lowest educated group had a more adverse cardiovascular risk factor profile compared to the highest educated group, and adjustment for these risk factors reduced the HR to 1.18 (95% CI 0.78-1.77). In analysis of individual risk factors, smoking and waist circumference explained most of the difference in CVD mortality between the highest and lowest education groups. Conclusions: Most of the excess CVD mortality in lower socioeconomic groups can be explained by known risk factors, particularly smoking and overweight. While targeting cardiovascular risk factors should not divert efforts from addressing the underlying determinants of health inequalities, it is essential that known risk factors are addressed effectively among lower socioeconomic groups.

Infrastructure sustainability : differential axial shortening of concrete structures

High density development has been seen as a contribution to sustainable development. However, a number of engineering issues play a crucial role in the sustainable construction of high rise buildings. Non linear deformation of concrete has an adverse impact on high-rise buildings with complex geometries, due to differential axial shortening. These adverse effects are caused by time dependent behaviour resulting in volume change known as ‘shrinkage’, ‘creep’ and ‘elastic’ deformation. These three phenomena govern the behaviour and performance of all concrete elements, during and after construction. Reinforcement content, variable concrete modulus, volume to surface area ratio of the elements, environmental conditions, and construction quality and sequence influence on the performance of concrete elements and differential axial shortening will occur in all structural systems. Its detrimental effects escalate with increasing height and non vertical load paths resulting from geometric complexity. The magnitude of these effects has a significant impact on building envelopes, building services, secondary systems, and lifetime serviceability and performance. Analytical and test procedures available to quantify the magnitude of these effects are limited to a very few parameters and are not adequately rigorous to capture the complexity of true time dependent material response. With this in mind, a research project has been undertaken to develop an accurate numerical procedure to quantify the differential axial shortening of structural elements. The procedure has been successfully applied to quantify the differential axial shortening of a high rise building, and the important capabilities available in the procedure have been discussed. A new practical concept, based on the variation of vibration characteristic of structure during and after construction and used to quantify the axial shortening and assess the performance of structure, is presented.

A numerical method to quantify differential axial shortening in concrete buildings

Differential distortion comprising axial shortening and consequent rotation in concrete buildings is caused by the time dependent effects of “shrinkage”, “creep” and “elastic” deformation. Reinforcement content, variable concrete modulus, volume to surface area ratio of elements and environmental conditions influence these distortions and their detrimental effects escalate with increasing height and geometric complexity of structure and non vertical load paths. Differential distortion has a significant impact on building envelopes, building services, secondary systems and the life time serviceability and performance of a building. Existing methods for quantifying these effects are unable to capture the complexity of such time dependent effects. This paper develops a numerical procedure that can accurately quantify the differential axial shortening that contributes significantly to total distortion in concrete buildings by taking into consideration (i) construction sequence and (ii) time varying values of Young’s Modulus of reinforced concrete and creep and shrinkage. Finite element techniques are used with time history analysis to simulate the response to staged construction. This procedure is discussed herein and illustrated through an example.