With the faster pace of China’s opening to the outside world, the contacts between Chinese enterprises and Portuguese speaking countries are becoming more and more frequent. Under this trend, how to further improve the quality of Portuguese classroom teaching is related to the development of students, enterprises and the long-term development of the whole country. This paper mainly focuses on the two aspects of “the main problems existing in Portuguese classroom teaching” and “the improvement countermeasures of Portuguese classroom teaching”. Combined with the current situation of Portuguese teaching, this paper puts forward targeted reform measures, in order to further optimize the Portuguese teaching system, with “student development”, “enterprise development” and take “national development” as the ultimate goal to cultivate a large number of high-quality Portuguese talents to the society.

With the progress of the times, the development of information technologies such as big data, artificial intelligence, and cloud computing is also in full swing. These new information technologies continue to impact China's existing traditional industries, enabling them to integrate and innovate, while also promoting China's entry into the digital economy era. For the accounting industry, this has also led to higher demands from society for accounting professionals, and most basic accounting personnel will face the dilemma of job changes as a result. This requires vocational colleges to consider more comprehensive training strategies when cultivating accounting professionals, so that accounting professionals can adapt to the new accounting functional requirements of contemporary society.

It is well known that determining the exact values of crossing number for circulant graphs is very difficult. Even so, some important results in this field are still proved. D.J. Ma was proved that the crossing number of C(2m + 2, m) is m + 1[8]. Then such problem for C(n, 3) was further solved [7]. Pak Tung Ho and X. Lin obtained accurate values for the crossover numbers of C (3m, m) and C (3m + 1, m)[4][5]. In this paper, as a complement, we show that the edges from the principal cycle of C(9, 3) do not cross each other in an optimal drawing.

As a key factor in the macroeconomic process, the interaction between public confidence and the commodity market, especially its impact on commodity facilitation returns and macroeconomic linkages, is worth exploring in depth. This study adopts the TVP-SV-VAR model to analyze the causal linkages, dynamic characteristics, and mechanisms of the interaction, and reveals the following core findings: (1) The economic background and information shocks contribute to the variations in the effects and orientations of the economic variables, which highlight the time-varying nature of the economic interactions. (2) Consumer and investor confidence exert heterogeneous influence on the macroeconomy, and their different responses to the negative effect of interest rates and convenience gains are particularly significant in the post-crisis recovery period. (3) In the short-term perspective, the influence of public confidence on monetary policy and inflation exceeds that in the medium and long term, highlighting the immediate sensitivity of individual economic behavior. (4) Since 2015, accommodative monetary policy has accelerated market capital flows, delaying the interaction between confidence indices and inflation, revealing policy time lag effects. (5) Convenience gains exhibit complex time-varying interactions with key economic parameters (interest rates, commodity prices, and inflation), with 2011 and 2014 displaying particular patterns, mapping differences between short- and long-term mechanisms, respectively. The study highlights the central role of consumer and investor confidence in the precise tailoring of macroeconomic policies, providing a scientific basis for policy forecasting and economic regulation, and contributing to economic stability. Meanwhile, the dynamic evolution of consumer confidence deepens market trend foresight, enhances the precision of market participants’ decision-making, and reinforces the resilience and predictability of economic operations.

Objective: To explore the influencing factors of mental health and the mediating role of self-compassion between family cohesion and mental health. Method: Family Cohesion Scale, Symptom Checklist, and Self-compassion Scale were used to investigate 593 college students in Zhejiang Province. Result: Family Cohesion was negatively correlated with mental health and positively correlated with Self-compass- ion among college students; Self-compassion was negatively correlated with mental health. Self-compassion fully mediates the relationship between the two. Conclusion: The path of family cohesion is indirect, and strengthening Self-compassion education can improve the mental health level of college students.

Combining physical, social, and economic elements, urban planning plays a critical role in creating sustainable, resilient, and livable urban environments. It encompasses the regulation of land use, infrastructure, transportation systems, and environmental resources, with a focus on sustainable urban design and green infrastructure. While progress has been made, there are still areas that have not been fully explored, including the integration of renewable energy sources and the development of urban environments that are resilient to environmental stresses. This study aims to analyze the direction and scope of urban planning research and to identify research gaps in this area. The method used is bibliometrics by analyzing data obtained from the Scopus database in January 2024. The results of this study showed that Yufeng Zhang, a professor at Wuhan University, China, was the most productive author in producing publications, namely 22 documents. In addition, the article produced by Qianqian Zhou is also influential in this research topic because it gets a number of citations, as high as 204 citations. Additionally, the results indicate the current focus of research on sustainability, adaptation to climate change, and technology in urban planning. These findings can guide future research, direct policy, and ensure an interdisciplinary approach to modern urban and regional challenges.