In this paper, we give a classification of all Mengerian \(4\)-uniform hypergraphs derived from graphs.

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.

The \( n \)-dimensional Möbius cube \( MQ_n \) is an important variant of the hypercube \( Q_n \), which possesses some properties superior to the hypercube. This paper investigates the fault-tolerant edge-pancyclicity of \( MQ_n \), and shows that if \( MQ_n \) (\( n \geq 5 \)) contains at most \( n-2 \) faulty vertices and/or edges then, for any fault-free edge \( uv \) in \( MQ_n^i (i=0,1) \) and any integer \( \ell \) with \( 7-i \leqslant \ell \leqslant 2^n – f_v \), there is a fault-free cycle of length \( \ell \) containing the edge \( uv \), where \( f_v \) is the number of faulty vertices. The result is optimal in some senses.

In a recent paper Cameron, Lakshmanan and Ajith [6] began an exploration of hypergraphs defined on algebraic structures, especially groups, to investigate whether this can add a new perspective. Following their suggestions, we consider suitable hypergraphs encoding the generating properties of a finite group. In particular, answering a question asked in their paper, we classified the finite solvable groups whose generating hypergraph is the basis hypergraph of a matroid.

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 \(n^2m(m-1) \equiv 0 \pmod{8}\).