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. By modeling directional variability in thermal conductivity using both uniform and Von Mises distributions, the study highlights the superiority of the Von Mises distribution in providing consistent and efficient thermal performance. The Von Mises distribution, known for its concentration around a mean direction, demonstrates a significant advantage over the uniform distribution, resulting in higher mean efficiency and lower variability. The findings underscore the importance of considering both stochastic effects and directional consistency in thermal systems, paving the way for more robust and reliable design strategies.

In the context of digital transformation, Chinese small and medium sized enterprises (SMEs) face significant challenges and opportunities in adapting to market dynamics and technological advancements. This study investigates the impact of coopetition strategy on the core competencies of SMEs, with a particular focus on marketing, technological, and integrative competencies. Data were collected from a sample of 300 SMEs in Anhui Province through an online survey, and reliability and validity were tested using SPSS and AMOS. The results indicate that dependency and trust significantly enhance the effectiveness of coopetition strategy from an external perspective, while managerial ambidexterity and strategic intent are critical internal factors driving the successful implementation of coopetition strategies. Both external and internal factors positively impact the core competencies of SMEs. Additionally, environmental uncertainty moderates the relationship between coopetition strategy and core competencies, underscoring the need for flexibility and adaptability in dynamic market environments. The findings suggest that SMEs can better integrate internal and external resources, optimize resource allocation, and improve operational efficiency through coopetition strategy, thereby enhancing their core competencies. This study provides valuable insights and practical guidance for policymakers and business practitioners aiming to support the digital transformation of SMEs.