An nontrivial extension of the maximal static flow problem is the maximal dynamic flow model, where the transit time to traverse an arc is taken into consideration. If the network parameters as capacities, arc traversal times, and so on, are constant over time, then a dynamic flow problem is said to be stationary. Research on flow in planar static network is motivated by the fact that more efficient algorithms can be developed by exploiting the planar structure of the graph. This article states and solves the maximum flow in directed (1, n) planar dynamic networks in the stationary case.

The European Union (EU) labor market needs a better-skilled workforce that can work in any of the Member States. In order to develop the skills and competencies of future competitors in this market, several student mobility programs have been set up in the EU, where they can travel to universities in partner countries to further their studies and enrich their academic performance, culture and knowledge. The best known of these programs is ERASMUS (European Region Action Scheme for the Mobility of University Students). Because Romania also participates in this program in the exchange of university students, the authors wanted, through this study, to highlight the benefits and challenges of participation in the program, to analyze how international mobilities are emotionally perceived by students and what are the behavioral reasons that determine Romanian students to choose a certain university as a study destination abroad. For this purpose, the authors conducted quantitative marketing research among students from the Transilvania University of Brasov who have been abroad with ERASMUS scholarships. The research results show that an important component in choosing a certain university is not the financial expense during the mobility as might have been expected, but rather the initial desire to study abroad. Students also consider the improvement of their academic performance as an equally important reason for embarking on mobility to the social aspect of getting to know other cultures.

The study examines the emotional and physiological effects of message framing in sustainability communication. Specifically, it explores how different image–message combinations shape consumer engagement by measuring physiological arousal (activation), and emotional resonance (impact) across various product categories. By using Galvanic Skin Response data combined with a hierarchical cluster analysis, the research provides insights into how individuals process sustainability information at both emotional and cognitive levels. The results reveal diverse and nuanced reactions shaped by the interaction of message framing, topic, and gender. The identification of seven distinct response patterns contributes to emerging consumer typologies in sustainability communication, offering practical value for organizations seeking to tailor messaging, enhance audience engagement, and encourage sustainable behavior.

This article states and solves the maximum flow in directed (1, n) planar dynamic networks with lower bounds. We present the case when the planar dynamic network is stationary. Finally, we present an example for this problem.

In the digital era, user-generated online reviews serve as a valuable resource for understanding visitor experiences in cultural institutions. This study analyses sentiments and thematic trends in TripAdvisor reviews of mountain museums, using Latent Dirichlet Allocation topic modelling and sentiment analysis. A dataset of 2157 reviews from ten museums was classified into local and non-local perspectives, revealing significant differences in visitor expectations. Findings indicate that local visitors prioritize historical authenticity and educational value, whereas non-local visitors emphasize aesthetic appeal, interactivity, and cultural immersion. Sentiment analysis highlights generally positive perceptions, with business travellers and groups of friends reporting the highest satisfaction levels. Comparative analysis across visitor types reveals distinct engagement patterns, with families valuing child-friendly exhibits, couples seeking cultural enrichment, and solo travellers focusing on intellectual depth. These insights inform strategic recommendations for museum management, including multilingual content, interactive elements, and guided tours dedicated to specific visitor profiles. Despite limitations related to lack of real-time feedback, this research demonstrates the potential of sentiment analysis in enhancing museum experiences. Future studies should integrate multimodal analysis and real-time tracking to further refine visitor experience evaluation.

We present an algorithm for finding maximum cut and an algorithm for finding minimum flow in directed s-t planar networks with arcs and nodes capacities. As a final part, we present an example for these two algorithms.