Meta-analysis was conducted to investigate the effects of static versus dynamic stretching on athlete agility. Keywords such as dynamic stretching, static stretching, athletes, and agility were searched through China Knowledge Network (CNKI), Wanfang, Pubmed, Web of Science, and EBSCO. Inclusion and exclusion criteria were established, and Endnote software was used to screen the literature, with statistical analysis performed using Stata and Revman. A total of 15 papers with 322 groups of experiments were included, with interventions typically performed three times a week. The quality of the included papers, assessed using Review Manager, showed all studies to be randomized controlled trials with low-risk indicators. Meta-analysis results indicated high heterogeneity with SMD=0.11 and significant differences (P<0.00001<0.05). The findings suggest that static and dynamic stretching, with an intervention period of about 15 weeks and a frequency of approximately three times per week, have a significant effect on athlete agility.

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 secret sharing, the relationships between participants and the information they hold can be modeled effectively using graph structures. Graphs allow us to visualize and analyze these relationships, making it easier to define access structures, optimize share distributions, and ensure security. This paper provides the first comprehensive review of existing research on the application of graph theory to secret sharing comparing different classic and modern approaches and analyzing the current litterature. Through this study we highlight the key advances and methodologies that have been developed, underscoring the pivotal role of graph theoretic approaches in enhancing the security and efficiency of secret sharing schemes. Furthermore, the review identifies open challenges and future research directions, providing insights into potential innovations that could further strengthen cryptographic practices. This work serves as a foundational resource for researchers and practitioners seeking to deepen their understanding of the intersection between graph theory and secret sharing, fostering the development of more robust and sophisticated cryptographic solutions.

Big data technology makes it possible to scientifically analyse a large amount of marketing data, which plays an important role in the development of marketing strategies for products and the improvement of marketing effects. In this paper, a marketing data stream analysis system is designed based on the stream analysis method. The system designs and optimises the marketing data storage and retrieval, data acquisition and streaming calculation engine to achieve real-time user behaviour data streaming analysis. The average response time accuracy of the system’s data can reach 96%, the throughput rate is 11.8% ahead of the maximum compared to the Word Count system, and the before-and-after ratios of the PUSH message click rate, the user registration success rate, the online shop attention rate, the returning customer rate, and the loyal customer rate are 1.03, 1.02, 1.27, 1.11, 1.27, and 1.78, respectively. It indicates that this paper’s design of the marketing data streaming analysis system has good performance and application effect.

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.

Chinese animation has long faced challenges, with foreign animation dominating the market and domestic animation struggling to compete. The rise of new media has driven the industrialization and branding of Chinese animation, linking it to complex social and cultural networks that shape its future competitiveness. Similarly, sports events, as cultural phenomena, hold both entertainment and cultural significance, reflecting societal modernization. This study categorizes mascot design features of sports events into appearance, color, and accessory characteristics, providing theoretical insights to enhance understanding of event culture. Experimental results show that an optimized cellular genetic algorithm improves mascot design, aligning with human aesthetics while promoting the spirit of sports globally.

A \(\mathcal{Y}\) tree on \(k\) vertices is denoted by \(\mathcal{Y}_k\). To decompose a graph into \(\mathcal{Y}_k\) trees, it is necessary to create a collection of subgraphs that are isomorphic to \(\mathcal{Y}_k\) tree and are all distinct. It is possible to acquire the necessary condition to decompose \(K_m(n)\) into \(\mathcal{Y}_k\) trees (\(k \geq 5\)), which has been obtained as \(n^2m(m-1) \equiv 0 \pmod{2(k-1)}\). It has been demonstrated in this document that, a gregarious \(\mathcal{Y}_5\) tree decomposition in \(K_m(n)\) is possible only if \(n^2m(m-1) \equiv 0 \pmod{8}\).

The λ-fold complete symmetric directed graph of order v, denoted ^λK_v^*, is the directed graph on v vertices and λ directed edges in each direction between each pair of vertices. For a given directed graph D, the set of all v for which ^λK_v^* admits a D-decomposition is called the λ-fold spectrum of D. In this paper, we settle the λ-fold spectrum of each of the nine non-isomorphic orientations of a 6-cycle.

In this paper, we provide a correction regarding the structure of negacyclic codes of length \(8p^s\) over \(\mathcal{R} = \mathbb{F}_{p^m} + u \mathbb{F}_{p^m}\) when \(p^m \equiv 3 \pmod{8}\) as classified in [1]. Among other results, we determine the number of codewords and the dual of each negacyclic code.

The multiplicative sum Zagreb index is a modified version of the well-known Zagreb indices. The multiplicative sum Zagreb index of a graph \(G\) is the product of the sums of the degrees of pairs of adjacent vertices. The mathematical properties of the multiplicative sum Zagreb index of graphs with given graph parameters deserve further study, as they can be used to detect chemical compounds and study network structures in mathematical chemistry. Therefore, in this paper, the maximal and minimal values of the multiplicative sum Zagreb indices of graphs with a given clique number are presented. Furthermore, the corresponding extremal graphs are characterized.