This research introduces a novel framework integrating stochastic finite element analysis (FEA) with advanced circular statistical methods to optimize heat pump efficiency under material uncertainties. The proposed methodologies and optimization focus on balancing the mean efficiency and variability by adjusting the concentration parameter of the Von Mises distribution, which models directional variability in thermal conductivity. The study highlights the superiority of the Von Mises distribution in achieving more consistent and efficient thermal performance compared to the uniform distribution. We also conducted a sensitivity analysis of the parameters for further insights. The results show that optimal tuning of the concentration parameter can significantly reduce efficiency variability while maintaining a mean efficiency above the desired threshold. This demonstrates the importance of considering both stochastic effects and directional consistency in thermal systems, providing robust and reliable design strategies.

The properties of the beta batteries are compared, which are made on the basis of the different β-isotopes with beta decay. Tritium and Ni-63 make it possible to make β-sources of high activity, without harmful associated emissions, with low self-absorption, emitting high-energy β-electrons that penetrate deep into the semiconductor and generate a large number of electron-hole pairs. The efficiency of beta batteries needs to be analyzed based on the real energy distribution of β-electrons. It makes possible to obtain the real value of the energy absorbed inside the β-source, correctly estimate the amount of self-absorption of the β-electrons and part of the β-electronsthere is a penetrate into the semiconductor, the number of electrons and holes that are generated in the semiconductor, and the magnitude of the idling voltage. Formulas for these quantities are calculated in this paper.

This paper examines the effect of governance in Sub-Saharan African (SSA) countries. Specifically, this study investigates (i) the interacting impact of government efficiency, regulatory quality, and the rule of law alongside other socioeconomic variables to determine foreign capital inflow (FCI) based on each economic SSA bloc; and (ii) the characteristic drivers of FCI, impacting economic growth in the SSA countries. Descriptive statistics, static models, least square dummy variables (LSDVs) and the dynamic system general method of moment (GMM) were employed as the study’s estimating techniques. Based on the result of the LSDV, food security and the rule of law significantly impact FCI in the sub-economic blocs in the region. Only six countries across the four economic blocs responded to food security and the rule of law in the model. The dynamic system-GMM provided evidence of five socioeconomic variables and three governance variables contributing to FCI. The findings revealed (i) regulatory quality and the rule of law are governance variables that significantly impacted FCI; and (ii) food security failed to significantly impact FCI in the SSA region. However, inflation, life expectancy, the human capital index, exchange rate and gross domestic product (GDP) growth impacted FCI significantly. In the aggregate, inflation, regulatory quality, exchange rate and the human capital index exhibited positive relationships, while other variables such as life expectancy, government effectiveness and the rule of law appeared significant but inversely impacted FCI in the SSA region. The key policy implication recommendation from this study is that a good legal framework could moderate the flow of foreign capital in favour of growth as it creates a strong foundation for sustainable economic development in the region.