Abstract The introduction of the “1+X” certificate system has put forward more new requirements for the training of international cruise crew management professionals in Chinese undergraduate colleges. Based on the requirements of the “1+X” certificate system, the integration of production and education has become an important path to cultivate high-quality and practical talents. Based on the talent training model of integration of production and education, this paper explores the impact of the “1+X” system on the talent training of undergraduate international cruise crew management majors, and puts forward three feasible suggestions, hoping to provide more references for the innovation and development of this major.

Abstract The path of Chinese-style modernisation is a great miracle in the history of the development of the Chinese nation and even the human society, and the generation of Chinese-style modernisation reveals three major logics, namely, the logic of history, the logic of theory and the logic of practice. Based on the national conditions of China, the theory of Chinese-style modernisation has unique connotations in five aspects: the main body of modernisation, the goal of modernisation, the support of modernisation, and the path of modernisation, which demonstrates the confidence in the road, the theory, the system, and the culture, and provides a fundamental guideline to promote the great rejuvenation of the Chinese nation, and contributes to Chinese wisdom to answer the problems of mankind, the global issues, and the world problems.

Abstract This paper deeply explores the use of financial engineering to manage enterprise risk related content. Firstly, the connotation of financial engineering and risk management is expounded comprehensively. Then it elaborates the effectiveness of financial engineering in the control process of price risk, quantity risk, investment risk, merger risk and agency risk. Then it analyzes the challenges faced by the application of financial engineering to manage enterprise risk. Based on the analysis of this paper, the purpose is to provide more references for enterprises to use financial engineering more effectively in risk management.

Abstract This paper explores the practical applications of level proximal subdifferentials in variational analysis and control theory, focusing on their role in handling nonsmooth optimization challenges and enhancing system stability. By examining their use in optimizing complex systems and ensuring robust control under uncertainty, the study demonstrates how level proximal subdifferentials improve adaptability and accuracy in real-world scenarios. Key applications include stability analysis in dynamic systems, adaptive control, and constraint handling. The paper also discusses computational challenges and proposes future research directions to broaden their applicability in high-stakes fields.

Abstract This paper firstly summarizes the accounting information system and audit, and then discusses the types and causes of audit risks, including the risks of the system itself, auditors, internal control, etc., and analyzes the reasons from the perspectives of technology, personnel quality, physical security and data protection. Finally, four effective strategies to avoid risks, namely strengthening internal control, attaching importance to external audit, building security guarantee mechanism and improving the quality of auditors, are put forward to provide reference for reducing the audit risk of accounting information system.

Abstract As a representative of Chinese culture, the architecture of the Forbidden City is a significant aspect of traditional ancient Chinese architecture.The patterns and shapes found on its buildings possess rich artistic connotations and considerable research value. This paper analyzes the cultural significance and architectural features of the elements within the Forbidden City. It extracts characteristic architectural elements from the Forbidden City and seeks to integrate these elements with modern clothing design. Furthermore, it explores the adaptability of traditional Forbidden City architectural elements when used in silk scarves as a medium. The aim is to promote the dissemination and development of traditional culture while providing innovative design concepts for contemporary fashion.

Abstract The Usage of Punctuation Marks (GB/T15834-2011) has been adopted as a national standard for many years; however, certain areas may benefit from further improvement. The main points are as follows: firstly, it is advisable to add an introduction to the dot mark “.”; secondly, it would be beneficial to expand the scope of the book title mark; thirdly, establishing a proper noun mark in modern Chinese texts is recommended; and fourthly, the repeated use and combination of question and exclamation marks should take into account the punctuation practices of ancient Chinese literature.

Abstract The innovative research and development of technology cannot be separated from the support of mathematical knowledge. Mathematics is a basic subject of science majors in colleges and universities. For college students, mathematics is a relatively difficult subject. The application of mathematical modeling can help students understand abstract mathematical knowledge and promote students to put mathematical knowledge into practice. Based on this, this paper discusses the specific application path of mathematical modeling in college mathematics teaching, in order to improve the quality of college mathematics teaching and enhance the effect of students’ mathematics learning.