The PBL teaching method emphasizes using specific problems as a guide in practical application, guiding students to achieve better teaching implementation results in practice. The integration of cross-border e-commerce and English teaching is a practical English course content in the teaching of English majors. In the current stage of English course teaching, it is an important method that is innovative and targeted to improve students' English course learning effectiveness. In the specific application process, the application of PBL teaching method requires teachers to provide important support for improving the teaching effectiveness of cross-border e-commerce English courses under the PBL model by building educational and teaching training bases, actively providing sufficient practical education guidance platforms, and emphasizing the innovation and richness of teaching evaluation links.

This study examines the adoption and usability of lifestyle (LS) apps, considering demographic factors like age and education that influence adoption decisions. The study employed a mixed-methods design, combining an experiment (spanning 14 weeks of app use) with semi-structured interviews and periodic measurements. The researchers employed the Mobile Application Usability Questionnaire (MAUQ) to identify pivotal aspects of standalone app usability, interface satisfaction, and usefulness at various stages of use, with a particular emphasis on the experiences of Hungarian students (n = 36). The results demonstrate that health-related factors have a significant impact on students’ behavior and evaluation of lifestyle apps over the 14-week period. Overall, the analyzed LS apps demonstrated positive outcomes in terms of supporting subject health and significantly improving the perceived health state. The findings highlight both practical and theoretical contributions to the field of mobile health applications, suggesting avenues for further research to either confirm or challenge existing theories.

The scientific objective of this study is to demonstrate how a hybrid photovoltaic-grid-generator microsystem responds under transient regime to varying loads and grid disconnection/reconnection. The object of the research was realized by acquiring the electrical magnitudes from the three PV systems (25 kW, 40 kW, and 60 kW) connected to the grid and the consumer (on-grid), during the technological process where the load fluctuated uncontrollably. Similar recordings were also made for the transient regime caused by the grid disconnection, diesel generator activation (450 kVA), its synchronization with PV systems, power supply to receivers, and grid voltage restoration after diesel generator shutdown. Analysis of the data focused on power supply continuity, voltage stability, and frequency variations. Findings indicated that on-grid photovoltaic systems had a 7.9% maximum voltage deviation from the standard value (230 V) and a frequency variation within ±1%. In the transient period caused by the grid disconnection and reconnection, a brief period with supply interruption was noted. This study contributes to the understanding of hybrid system behavior during transient regimes.

The article undertakes an exploration into the rather unexpected progressiveness exhibited by courts across the globe in bestowing protection upon LGBTQ rights. A three-pronged study, which encompasses an examination of the theoretical rationales, empirical investigations, and doctrinal underpinnings of the augmentation of LGBTQ rights in diverse locales, is executed. It is hypothesized that a prima facie paradox emerges, whereby LGBTQ rights have been safeguarded and advanced in an extraordinary fashion, while concurrently, a discernible general trend of deviation from liberal constitutionalism, rights safeguarding mechanisms, and the rule of law is observable in other arenas. This article scrutinizes this contention and discovers that it is substantiated by case law from various regions. Critical theory and Butler’s theory of performativity potentially offer the most cogent explanations for this paradox. They have led to the social embrace of LGBTQ rights, while simultaneously, the enactment or amplification of these rights even in illiberal states furnishes an effortless ‘triumph’ for illiberal political actors, which can be employed as a countermeasure against assaults on their liberal and democratic reputations.

With the rapid development of modernization and the reform and development of quality education, the main direction and goal of vocational colleges in the new era is to cultivate high-level skilled talents required by the times. With the development of globalization and the refined division of labor in industrial technology, the requirements of various industries for high-level skilled talents with the ability to adapt to market development are gradually increasing. This article focuses on exploring and analyzing the demand for hospital imaging technology talents under the rapid development of the new era industry, and discovering the problems in talent cultivation in vocational colleges. In response to the existing problems, actively utilizing college resources and practical opportunities, innovating the college school cooperation mode and teaching methods for imaging technology majors in vocational colleges, and gradually expanding into a standardized, scientific, and developable college cooperation mode for vocational education, Implement the national strategic plan for cultivating quality talents in vocational colleges, focus on doing a good job in the work of "cultivating morality and talents", adhere to the "three education" reform, and improve the quality of talent cultivation.

Under the background of the continuous development of science and technology, the era of big data has come in an all-round way, and big data technology has also been widely used in the education industry. The course of financial management in applied colleges and universities is a highly applied course, which focuses on the substance of the course. Teachers need to create a good learning environment for students with the help of information technology, and constantly cultivate students' professional skills and professionalism. In order to improve the quality of financial management courses in colleges and universities, this paper mainly analyzes the management courses in application-oriented colleges and universities, expounds the factors affecting the practical teaching quality of management courses in colleges and universities, and analyzes the teaching methods of management courses in application-oriented colleges and universities. Finally, it is concluded that only when teachers constantly improve their teaching level, can students' learning level be improved by combining theory with practice.