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Let $\mathcal {K}_u$ denote the class of all analytic functions f in the unit disk $\mathbb {D}:=\{z\in \mathbb {C}:|z| , normalised by $f(0)=f'(0)-1=0$ and satisfying $|zf'(z)/g(z)-1| in $\mathbb {D}$ for some starlike function g. Allu, Sokól and Thomas ['On a close-to-convex analogue of certain starlike functions', Bull. Aust. Math. Soc. 108 (2020), 268–281] obtained a partial solution for the Fekete–Szegö problem and initial coefficient estimates for functions in $\mathcal {K}_u$ , and posed a conjecture in this regard. We prove this conjecture regarding the sharp estimates of coefficients and solve the Fekete–Szegö problem completely for functions in the class $\mathcal {K}_u$. [ABSTRACT FROM AUTHOR]

In this paper, we study the following fractional Choquard equation with weight (−Δ)su=1|x|N−α∗h(x)|u|ph(x)|u|p−2uinℝN,$$ {\left(-\Delta \right)}&#x0005E;su&#x0003D;\left(\frac{1}{{\left&#x0007C;x\right&#x0007C;}&#x0005E;{N-\alpha }}\ast h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;p\right)h(x){\left&#x0007C;u\right&#x0007C;}&#x0005E;{p-2}u\kern0.5em \mathrm{in}\kern0.5em {\mathrm{\mathbb{R}}}&#x0005E;N, $$where 02s,p>2,α>0$$ 02s,p>2,\alpha >0 $$ and h$$ h $$ is a positive weight function satisfying h(x)≥C|x|a$$ h(x)\ge C{\left&#x0007C;x\right&#x0007C;}&#x0005E;a $$ at infinity, for some a≥0$$ a\ge 0 $$. We establish, in this paper, a Liouville type theorem saying that if maxN−4s−2a,0<α

Mathematics is traditionally considered necessary for engineering courses. Over the last three decades, the mathematics requirements for entry into engineering programmes has steadily weakened in Australia. Further, the mathematics component of engineering programmes has progressively decreased. This research aims to investigate the following two questions. First, is mathematics a barrier for students to complete an engineering programme? And second, is performance in mathematics associated with performance in engineering? We identified the significant factors associated with weighted average mark and the completion status of engineering studies at both an undergraduate level and a Masters level. Of particular interest was the students' mathematical background. Furthermore, a survey of students enrolled in engineering at the University of Western Australia was conducted to obtain more in depth views of student attitudes and perceptions towards how mathematics has affected their engineering studies. Binary logistic models were fitted to the survey data. Additionally, focus group interviews were conducted to gain insight on student perspectives regarding the effectiveness of mathematics teaching in engineering. The results are discussed in relation to the importance of mathematics and statistics for the engineering curriculum. [ABSTRACT FROM AUTHOR]

Background: Computer‐based assessment allows for the monitoring of reader behaviour. The identification of patterns in this behaviour can provide insights that may be useful in informing educational interventions. Objectives: Our study aims to explore what different patterns of reading activity exist, and investigates their interpretation and consistency across different task sets (units), countries, and languages. Three patterns were expected: on‐task, exploring and disengaged. Methods: Using log data from the PISA 2012 digital reading assessment (9226 students from seven countries), we conducted hierarchical cluster analyses with typical process indicators of digital reading assessments. We identified different patterns and explored whether they remained consistent across different units. To validate the interpretation of the identified patterns, we examined their relationship to performance and student characteristics (gender, socio‐economic status, print reading skills). Results and Conclusions: The results indicate a small number of transnational clusters, with unit‐specific differences. Cluster interpretation is supported by associations with student characteristics—for example, students with low print reading skills were more likely to show a disengaged pattern than proficient readers. Exploring behaviour tended to be exhibited only once across the three units: It occurred in the first unit for proficient readers and in later units for less skilled readers. Major Takeaways: Behavioural patterns can be identified in digital reading tasks that may prove useful for educational monitoring and intervention. Although task situations are designed to evoke certain behaviours, the interpretation of observed behavioural patterns requires validation based on task requirements, assessment context and relationships to other available information. Lay Description: What is already known about the subject matter?: Students differ in how they read, comprehend and use digital information.Indicators from process data provide insight about how students engage with digital reading tasks. What does this paper add to the subject matter?: Based on multiple process indicators, a small number of clusters indicating different behavioural activity can be distinguished.These clusters can be described as on‐task, passive, hasty, exploring, disengaged, persistent and lost interest.A meaningful interpretation of the clusters must consider the requirements of the underlying tasks. Implications for practice and/or policy: Knowledge of how students engage with digital resources may provide useful feedback for teachers to guide students' learning or intervene when they struggle.Educational monitoring: The high comparability of country‐specific results suggests an invariant set of solution strategies in the digital reading assessment. [ABSTRACT FROM AUTHOR]

Summary: Background: Evidence for longitudinal associations between childhood weight status and academic achievement remains unclear due to considerable heterogeneity in study design, measures of academic achievement and appropriate categorization of weight status. Objective: To examine longitudinal associations between childhood weight status (underweight, healthy weight, overweight/obese) and academic achievement in the transition from preschool to primary (elementary) school among Australian school children. Methods: Data were from the Healthy Active Preschool and Primary Years study. Height and weight, for calculating BMI were measured at baseline (preschool age 3–5 years; 2008/9) and follow‐up (primary school age 6–8 years; 2011/12). Academic achievement was measured at age 9 years. Results: No associations between BMI z‐score or weight category in the preschool years and later NAPLAN scores were found for boys. For girls, having a higher BMI z‐score (B = −13.68, 95%CI: −26.61, −0.76) and being affected by overweight (B = −33.57, 95%CI: −61.50, −5.24) in preschool was associated with lower language scores. Remaining affected by overweight from preschool to primary school was associated with lower numeracy (B = −25.03, 95%CI: −49.74, −0.33), spelling (B = −33.5, 95%CI: −63.43, −3.58), language (B = −37.89, 95%CI: −72.75, −3.03) and total achievement scores (B = −24.24, 95%CI: −44.85, −3.63) among girls. For boys, becoming affected by overweight was associated with lower spelling (B = −38.76, 95%CI: −73.59, −3.93) and total achievement scores (B = −27.70, 95%CI: −54.81, −0.58). Conclusions: Associations between being affected by overweight/obesity and poorer academic achievement were more pronounced in girls than boys, indicating potentially inequitable impacts of excess weight and highlighting the greater need for intervention among girls. However, stronger study designs are needed to confirm our findings. [ABSTRACT FROM AUTHOR]

An oriented graph is called singular or nonsingular according as its adjacency matrix is singular or nonsingular. In this note, by a new approach, we determine the singularity of oriented quasi-trees. The main results of Chen et al. ['Singularity of oriented graphs from several classes', Bull. Aust. Math. Soc. 102 (1) (2020), 7–14] follow as corollaries. Furthermore, we give a necessary condition for an oriented bipartite graph to be nonsingular. By applying this condition, we characterise nonsingular oriented bipartite graphs $B_{m,n}$ when $\min \{m,n\}\leq 3$. [ABSTRACT FROM AUTHOR]

In Australia, there have been a growing number of nature-based early childhood education initiatives [Alme, H., and M. A. Reime. 2021. "Nature Kindergartens: A Space for Children's Participation." Journal of Outdoor and Environmental Education 24: 113–131]. Research into early years' nature education internationally remains under-theorised particularly in STEM teaching and learning. The nature or bush kindergarten programme (often referred to as 'bush kinders' in the Australian context), is one such programme where nature play and education occur. This paper considers how children's mathematical thinking develops through their time spent in bush kinder settings. Using an ethnographic lens, this longitudinal study is the first of its type in Australia with a focus on STEM in bush kinders. In this paper, eight 'powerful mathematical ideas' are used to analyse how educators can approach teaching mathematics with only what nature provides. The paper reports one main finding, that bush kinders provide opportunities for children through educator support to build mathematical understandings through nature play. Drawing on fieldwork data and the analysis of research literature, this paper contributes to the conceptualisation of mathematics in early childhood nature play and bush kinder programmes. [ABSTRACT FROM AUTHOR]

While international research has demonstrated that ability grouping is inequitable, Australian research has often overlooked equity concerns, predominantly focusing on studying the benefits of grouping for students perceived to have high ability, especially in mathematics. This paper investigates the effect that mathematics ability grouping has on senior secondary mathematics participation for low and middle grouped students in New South Wales, Australia. We drew on interviews about mathematics participation with 85 students and 22 mathematics teachers from 11 government high schools. Our thematic analysis of these data identified that secondary school grouping practices often serve to entrench student interest and/or performance from primary school. This has consequences for many students, with a differentiated curriculum in Years 9 and 10 precluding low and middle grouped students from participating in high-level mathematics when they reach senior secondary school. These findings raise serious equity questions about the current push in Australia for universities to re-introduce high-level mathematics as a prerequisite to entering certain degrees. We argue that stakeholders need greater awareness of the consequences of ability grouping and that those seeking to lift post-compulsory mathematics participation should be targeting primary and early secondary school. [ABSTRACT FROM AUTHOR]

This article describes the approach used to assess the performance of a Fourier transform infrared (FTIR) and principal component regression (PCR) chemometric method when measuring respirable quartz, kaolinite, and coal in samples from a variety of mines from different countries; relative to target assigned values determined using X-ray diffraction (XRD). For comparison, FTIR results using the partial least squares regression (PLSR) method are also available. Bulk dusts from 10 Australian mines were scanned using XRD and grouped into three sets based on the levels of quartz, kaolinite, and feldspar within their crystalline mineral composition. Prediction samples were generated from 5 of these Australian mine dusts, Durrans coal dust, 2 mine dusts from the UK, and a single South African mine dust (71 samples in total) by collecting the aerosolized respirable dust onto 25-mm diameter polyvinylchloride filters using the Safety in Mines Personal Dust Sampler (SIMPEDS) operating at 2.2 l min−1. The predicted values from the FTIR chemometric methods were compared with assigned target values determined using a direct on-aerosol filter XRD analysis method described in Method for the Determination of Hazardous Substances (MDHS) 101. Limits of detection (LOD) and uncertainty values for each analyte were calculated from a linear regression between target and predicted values. The uncertainty was determined using the calibration uncertainty equation for an unweighted regression. FTIR results from PCR and PLSR are very similar. For the PCR method, the LOD for quartz, kaolinite, and coal were 5, 25, and 71 µg, respectively. For quartz, an LOD of 5 µg corresponds to an airborne quartz concentration of 10 µg m−3, assuming a 4-h sampling time and collection flow rate of 2.2 l min−1. The FTIR measurement met the expected performance criteria outlined in ISO 20581 when sampling quartz for more than 4 h using a flow rate of 2.2 l min−1 at a concentration of 0.1 mg m−3 (100 µg m−3), the current workplace exposure limit in Great Britain. This method met the same performance criteria when measuring exposures at the Australian Workplace Exposure Standard (WES) concentration of 0.05 mg m−3, although in this case a sampling period greater than 8 h was needed. [ABSTRACT FROM AUTHOR]

This paper is intended to provide a source of critical and theoretical reflection on the current mathematics educational objectives for Indigenous students in Australia, which are premised on acceptance of underlying concepts of 'equity'. It is not the intention of this paper to identify 'how' Indigenous knowledge can be positioned within mathematics curricula, as this would entail a philosophical inquiry much deeper than has been afforded thus far. The intent here is a consideration, facilitated through the lens of key concepts of Foucault, of some of the boundaries currently shaping the ways in which this positioning is being influenced in the mathematics, albeit neoliberal education context. Acknowledging the interplay between the social, and unconsciously shaped adoptions of what can be considered truth; knowledge; and therefore power, is a first step toward developing the openness of heart and mind needed to make real and transformative changes to education for future societies. [ABSTRACT FROM AUTHOR]