The study examines the impact of various theories on the reflection and transmission phenomena caused by obliquely incident longitudinal and transverse waves at the interface between a continuously elastic solid half-space and a thermoelastic half-space, using multiple thermoelastic models. Numerical calculations reveal that the thermoelastic medium supports one transmitted transverse wave and two transmitted longitudinal waves. The modulus of amplitude proportions is analyzed as a function of the angle of incidence, showing distinct variations across the studied models. Energy ratios, derived from wave amplitudes under consistent surface boundary conditions for copper, are computed and compared across angles of incidence. The results demonstrate that the total energy ratio consistently sums to one, validating energy conservation principles. Graphical comparisons of amplitude proportions and energy ratios for SV and P waves across different models illustrate significant differences in wave behavior, emphasizing the influence of thermoelastic properties on wave transmission and reflection.

The study explores the relationship between authentic leadership, psychological capital, and work engagement among educators in the Makhado Municipality. The primary aim was to assess how authentic leadership influences educators’ psychological capital and examine how psychological capital impacts work engagement. A quantitative research design was employed, utilizing a survey-based approach to collect data from a sample of educators across 15 primary schools within the Makhado Municipality. Structural Equation Modeling was used to analyze the data and test the relationships between authentic leadership, psychological capital, and work engagement. Results indicate that authentic leadership has a significant positive influence on the psychological capital of educators. In turn, psychological Capital was found to have a strong positive impact on work engagement, suggesting that educators who perceive their leaders as authentic are more likely to experience higher levels of psychological well-being and engagement in their work. This study contributes to the literature on leadership and educator well-being by demonstrating the value of authentic leadership in promoting a supportive work environment that enhances educators’ psychological capital and engagement. The educational management and policy implications emphasize the need for leadership development programs that foster authentic leadership behaviors to improve educator performance and overall school effectiveness.

Electricity consumption in Europe has risen significantly in recent years, with households being the largest consumers of final electricity. Managing and reducing residential power consumption is critical for achieving efficient and sustainable energy management, conserving financial resources, and mitigating environmental effects. Many studies have used statistical models such as linear, multinomial, ridge, polynomial, and LASSO regression to examine and understand the determinants of residential energy consumption. However, these models are limited to capturing only direct effects among the determinants of household energy consumption. This study addresses these limitations by applying a path analysis model that captures the direct and indirect effects. Numerical and theoretical comparisons that demonstrate its advantages and efficiency are also given. The results show that Sub-metering components associated with specific uses, like cooking or water heating, have significant indirect impacts on global intensity through active power and that the voltage affects negatively the global power (active and reactive) due to the physical and behavioral mechanisms. Our findings provide an in-depth understanding of household electricity power consumption. This will improve forecasting and enable real-time energy management tools, extending to the design of precise energy efficiency policies to achieve SDG 7’s objectives.

The maize commodity is of strategic significance to the South African economy as it is a stable commodity and therefore a key factor for food security. In recent times climate change has impacted on the productivity of this commodity and this has impacted trade negatively. This paper explores the intricate relationship between climatic factors and trade performance for the South African maize. Secondary annual time series data spanning 2001 to 2023, was sourced from an abstract from Department of Agriculture, Land Reform and Rural Development (DALRRD) and World Bank’s Climate Change Knowledge Portal. Autoregressive Distributed Lag (ARDL) cointegration technique was used as an empirical model to assess the long-term and short-term relationships between explanatory variables and the dependent variable. Results of the ARDL model show that, average annual rainfall (β = 2.184, p = 0.056), fertilizer consumption (β = 1.919, p = 0.036), gross value of production (β = 1.279 , p = 0.006) and average annual surface temperature (β = −0.650, p = 0.991) and change in temperature for previous years, (β = −0.650, p = 0.991) and the effects towards coefficient change for export volumes, (β = 0.669, p = 0.0007). In overall, as a recommendation, South African policymakers should consider these findings when developing strategies to mitigate the impacts of some of these climatic factors and implementing adaptive strategies for maize producers.