Let \(R\) be a commutative ring. The principal intersection graph of a commutative ring \(R\), noted \(G_{c}(R)\), consists of all proper ideals of \(R\) as vertices. Two distinct vertices \(I\) and \(J\) are adjacent if \(I\cap J \neq 0\) and either \(I\) or \(J\) is a principal (cyclic) ideal. In this paper, we investigate some properties from graph theory of \(G_{c}(R)\) and its algebraic properties where \(R\) is a ring.

With the direct support of the Party and the state, after more than 20 years of development, universities have established educational ideas and political theories, which are “facing the problems of curriculum reform”, “teaching beliefs and politics”, and “deviation between teaching and related research”. On the basis of years of teaching practice, they creatively put forward scientific concepts based on beliefs and political characteristics, and an important method to help understand the current situation, In recent years, great progress has been made in relevant research, but there are still many defects, which seriously affect the sustainable and healthy development of ideological and political theory in universities. This paper takes the computerization and algorithm model of complex information network as the starting point, and the best method of science education and politics as the research standard. The document combines the principle of combining scientific and humanistic methods with the best method of university education knowledge and politics, provides the best method for the knowledge and political model of education, and analyzes the credibility. The empirical results show that the accuracy of the ideal model is 91%. The improved computerized model provides supporting data for stimulating the intellectual and political vitality of university theoretical courses, improving the educational effect, strengthening educational ideas and policies, and ensuring the quality of university education.

Special attention has been paid to China’s socio-economic development, the gradual improvement of the living standards of the population, and the family and society have begun to pay attention to preschool education. However, the process is affected by a series of factors, such as school factors, family factors, teachers and social factors, which reduce the quality of kindergarten brand image and learning and are not conducive to effectively empowering children in various fields. To effectively accomplish the goals of kindergarten, teachers should make use of the comprehensive nurturing value of labor education to maximize and optimize the value of education. Kindergarten brand image evaluation is an important part of kindergarten teaching, which can help teachers and researchers better understand how effective kindergarten brand image is and how to develop. This paper discusses the problems existing in China’s kindergarten brand image evaluation, and puts forward an evaluation method of kindergarten brand image quality based on support vector mechanism (SVM) and component analysis, so as to improve the evaluation quality.

The promotion of industrial digital transformation is an important breakthrough in the change of economic structure and physical space layout, which can promote the entire industrial chain to the high-end value chain and win more profit space and voice for the integration of domestic and international industries into the international cycle. This study takes the cities in the Yangtze River Delta Economic Belt as an example to deeply explore the spatial effect of digital transformation on the healthy transformation of traditional industrial structure, and constructs relevant spatial coupling models to carry out empirical verification by taking the opportunity of putting forward relevant assumptions. The experimental results show that the model is significant at a significance level of more than 5%, which is suitable for the selection of spatial measurement model. The mean square error of its network simulation output is 0.1333, which verifies the expected hypothesis and proves that the digital transformation of the model has a significant spatial driving effect on industrial upgrading.

At present, electric shock accidents are still the main safety issue for distribution workers. In recent years, the promotion of video AI applications has made it possible to detect whether the human body has crossed the safety line, and how to detect the actual height of the workers and the actual spatial distance between them and live equipment and live lines has become a challenge for researchers. Therefore, this article proposes to use LiDAR, edge processing module, and warning module to build a pre control device for safe operation behavior in power distribution scenarios, scan the power distribution operation scene in real time, use deep learning methods to identify objects such as distribution stations, human bodies, high-voltage equipment, and transmission lines in the point cloud, and calculate the spatial distance between operators and high-voltage equipment and lines in the station area through the edge point coordinates of object point cloud aggregation. When the spatial distance approaches or exceeds the voltage safety distance, the warning module sends voice reminders to achieve the pre control effect of safe operation behavior. The experimental results show that the device can significantly reduce the false alarm rate compared to the video scheme, accurately detect the actual distance between operators and high-voltage live equipment and high-voltage transmission lines in the substation area, and provide timely and effective alarm prompts. Therefore, this scheme can be applied in power distribution operation scenarios to protect the personal safety of workers.

The scientific knowledge graph is an emerging research method in this context. In the research of physical education teaching, the research and sorting out of the research results of physical education teaching in my country from the perspective of scientometrics and information visualization is still slightly insufficient. The similarity between the frontiers of physical education teaching research in China and the United States in the past five years is that both countries have paid more attention to research topics such as physical education teaching methods and physical education courses. This paper proposes a rough set knowledge reduction algorithm based on improved genetic algorithm. The support and importance of conditional attributes to decision attributes are introduced into the information system, which are added to the genetic algorithm as heuristic information, and the concepts of population dissimilarity and individual dissimilarity are proposed to improve the genetic algorithm. The research on school physical education in my country is biased towards problem research, while the research on physical education teaching methods in the United States is biased towards student health; In addition, starting from the national conditions, the hotspots in the field of physical education teaching in my country tend to be “Sports and Health Curriculum Standards”, physical education teachers, physical education ideas, educational theories and college sports, while the hotspots in the field of physical education teaching in the United States tend to be physical activity, children and adolescents , students, women, exercise education, physical education, self-determination theory, and the integration of psychological motivation and physical education. Experimental data analysis my country’s physical education curriculum research should appropriately increase the attention to the details of physical education curriculum, and my country’s physical education teaching practice research should appropriately increase the research on physical education from the perspective of public health.

In recent years, ideological and political theory (IPE) education has received more and more attention. System theory can well construct the IPE teaching mode, so we need to have a good grasp of system theory. This paper starts with the significance of system theory in the practical teaching of IPE, finds the IPE curriculum that conforms to system theory, and constructs the basic mode of practical teaching of IPE on this basis. Using the idea of a multi-level fuzzy comprehensive evaluation to quantify teachers’ teaching quality, this paper establishes an algorithm model to quantitatively measure teachers’ teaching quality fuzzy.

In the context of today’s big data and information age, blended learning has gradually entered people’s vision. At present, the number of business Japanese learners in China is increasing, and the breadth and depth of business Japanese education are expanding in all aspects. Therefore, people gradually pay attention to the practice and exploration mode of Internet, Japanese teaching and mixed learning, and learning evaluation is an important part of them. In this study, the construction of hybrid learning evaluation index is studied in the form of algorithm optimization and experimental verification. It takes blended learning as the evaluation object, aiming to build an evaluation index system of blended learning and help teachers implement high-quality blended learning. Based on the learning theory, this study also proposes the guiding strategies for senior high school students’ business Japanese learning from the perspective of schools, teachers and students themselves. Through empirical research and hypothesis verification, it provides reference for business Japanese education and learning in senior high schools in China. The experimental results show that the Nivre model after our calculation and optimization is based on the new education concept and the era development environment, and constantly improves the mixed learning mode, which improves the quality of business Japanese learning. Through correlation analysis and reliability and validity tests, the accuracy of the model in different test sets exceeded 92\%, which was in line with expected assumptions and empirical tests. The model has certain practical value.

With development of Internet of Things, big data and artificial intelligence, cell phone signaling data, point-of-interest data and machine learning methods have been widely used in research of various fields of transportation. The use of big data processing techniques and machine learning methods to mine intercity travel data collected by various types of traffic detectors provides a new way of thinking to study travel mode selection behavior. In this paper, we pre-processed cell phone signaling data, geospatial data and interest point data around three aspects: personal attributes, travel attributes and travel mode attributes, and designed intercity travel target group extraction, travel chain extraction, travel mode extraction and travel purpose extraction algorithms, which provide basis for travel feature analysis and travel mode choice behavior prediction modeling.

With the construction of the national discourse power, the international communication of German-language has also attracted the attention of the public, and its own communication attributes and characteristics have also become a hot topic around the world. A machine learning development process includes operations such as data preprocessing, feature engineering, model design, and super parameter optimization. Changes in the configuration of each operation may affect the final quality of the model. Nor is it mainly the problem of teachers’ teaching, but the communication barrier caused by cultural differences. We can see that there are still many obstacles and misunderstandings in language, thought, cross-cultural communication and knowledge in many communication occasions between China and Germany. Through reviewing and summarizing the previous studies on intercultural communication, this paper analyzes the current situation of intercultural communication studies, points out the problems existing in the current research, and tries to put forward the cultivation methods of intercultural communication.