We use a dynamic programming algorithm to establish a new lower bound on the domination number of complete cylindrical grid graphs of the form \(C_n\square P_m\), that is, the Cartesian product of a path and a cycle, when \(n\equiv 2\pmod{5}\), and we establish a new upper bound equal to the lower bound, thus computing the exact domination number for these graphs.

In this paper, we address computational questions surrounding the enumeration of non-isomorphic André planes for any prime power order \(q\). We are particularly focused on providing a complete enumeration of all such planes for relatively small orders (up to 125), as well as developing computationally efficient ways to count the number of isomorphism classes for other orders where enumeration is infeasible. André planes of all dimensions over their kernel are considered.

We use a dynamic programming algorithm to establish a lower bound on the domination number of complete grid graphs of the form \(C_n\square P_m\), that is, the Cartesian product of a cycle \(C_n\) and a path \(P_m\), for \(m\) and \(n\) sufficiently large.

With the increasingly frequent exchanges between countries, my country’s demand for high-quality English translators has greatly increased. However, an important problem we are currently facing is that China’s translation talents are far behind the demand. An important reason for this phenomenon is that the traditional translation teaching is difficult to cultivate translators who can meet the market demand. Therefore, it is necessary to improve the traditional translation teaching mode. Translation teaching for English majors is an important part of translation teaching. Therefore, after evaluating the speech characteristics and speech data, this document first proposes a translation classification error detection model based on mfcc-rf. The acoustic function of the extracted 39 dimensional Mel inverse spectral coefficient is the input of the random forest classifier, and a classification error detection model is established. By analyzing the experimental results, the MFCC radio frequency translation error detection model has achieved high classification error detection accuracy under three types of errors (rising, falling and shortening). The experimental results show that, with semantic similarity as the design principle of distractors, using the word vector training method of the context word prediction model to automatically generate distractors can ultimately improve the comprehensive training efficiency of college English majors’ translation ability.

A node in the \(n\)-dimensional hypercube \(Q_n\) is called an odd node (resp. an even node) if the sum of all digits of the node is odd (resp. even). Let \(F\subset E(Q_n)\) and let \(L\) be a linear forest in \(Q_n-F\) such that \(|E(L)|+|F|\leq n-2\) for \(n\geq 2\). Let \(x\) be an odd node and \(y\) an even node in \(Q_n\) such that none of the paths in \(L\) has \(x\) or \(y\) as internal node or both of them as end nodes. In this note, we prove that there is a Hamiltonian path between \(x\) and \(y\) passing through \(L\) in \(Q_n-F\). The upper bound \(n-2\) on \(|E(L)|+|F|\) is sharp.

As a product of the revolutionary war years, red culture, with its strong vitality, strong cohesion and extraordinary charm, with its incomparable positive energy, resists vulgar and flattering culture, promotes people to rebuild their faith, purify their minds, stimulate their motivation, and promote the process of cultural power. Yan’an, represented by red culture, is rich in resources. This is the holy land of Chinese revolution, the first batch of famous historical and cultural cities named by the State Council, and the three major education bases of patriotism, revolutionary tradition, and Yan’an spirit. The development and utilization of such resources have great political, cultural, educational and economic values. This research is based on the development of red culture, and uses the distributed machine learning system to realize in the system architecture of parameter server. In the distributed system set in this study, node downtime and network interruption are random. When the parameter server system adopts static scheduling, it leads to poor scalability and robustness. The experimental results show that under the intelligent simulation of machine learning system, the development of red culture resources meets the expected assumptions, and the accuracy of the model is relatively high.

In this paper, we introduce a class of restricted symmetric permutations, called half-exceeded symmetric permutations. We deduce the enumerative formula of the permutations of \(\{1,2,\ldots,2n\}\) and give it a refinement according to the distribution of the inverse pairs. As a consequence, we obtain new combinatorial interpretations of some well-known sequences, such as Stirling numbers of the second kind and ordered Bell numbers. Moreover, we introduce the ordered Stirling number of the second kind and establish a combinatorial proof of the recursive relation of the sequence.

The total labeling of a graph \(G=(V,E)\) is a bijection from the union of the vertex set and the edge set of \(G\) to the set \(\{1,2,\dots,|V(G)|+|E(G)|\}\). The edge-weight of an edge under a total labeling is the sum of the label of the edge and the labels of the end vertices of that edge. The vertex-weight of a vertex under a total labeling is the sum of the label of the vertex and the labels of all the edges incident with that vertex. A total labeling is called edge-magic or vertex-magic when all the edge-weights or all the vertex-weights are the same, respectively. When all the edge-weights or all the vertex-weights are different then a total labeling is called edge-antimagic or vertex-antimagic total, respectively.

In this paper we deal with the problem of finding a~total labeling of some classes of graphs that is simultaneously vertex-magic and edge-antimagic or simultaneously vertex-antimagic and edge-magic, respectively.
We show several results for stars, paths and cycles.

This study presents a pioneering federated multi-modal data classification model tailored for smart optical cable monitoring systems. By harnessing federated learning techniques, the model ensures data privacy while achieving performance on par with centralized models. Through comprehensive experiments spanning various modalities, including vision and auditory data, our approach showcases promising outcomes, as evidenced by accuracy and precision metrics. Furthermore, comparative analyses with centralized models highlight the superior data security and reduced network strain offered by federated learning. Moreover, we delineate the design and deployment of a smart optical cable monitoring system leveraging edge computing, accentuating the pivotal role of information technology in elevating operational efficiency within the cable monitoring domain. Through meticulous analysis and simulations, our proposed system adeptly monitors environmental variables, thereby bolstering safety and efficiency in smart optical cable monitoring applications.

The created public art sculpture is a material form that expresses the public spirit of the city. This paper proposes a deep model capable of enhancing the aesthetic quality of public art sculptures. The model uses the inverse mapping network of the augmented network to weaken the restriction of paired data sets required for training, and at the same time designs an effective loss function, that is, constructs the color and texture losses that are actively learned in training through generative adversarial rules, and enhances generative sculpture. The total variational loss of smoothness that improves the aesthetic quality of the sculpture to some extent. On this basis, this paper improves the design idea of content consistency loss. Experiments on the interaction between public art sculptures and the urban environment and the enhancement of aesthetics.