Three remarkable determinant identities of skew–symmetric matrices are reviewed in a more transparent manner.

In graph theory, the center function identifies a set of vertices in a connected graph G that minimizes the maximum distance from any other vertex. We examine the behavior of the center function on connected graphs through a set of axioms. While universal axioms apply to all connected graphs, they cannot fully characterize certain graphs. To address this limitation, non-universal axioms for specific graph classes were introduced. This study is focused on establishing an axiomatic characterization of the center function on fan graphs by utilizing a combination of universal and non-universal axioms.

To counter threats to low-orbit communication satellites from hacker attacks and spectrum interference, this study develops an adversarial sample detection model using a variational self-encoder and a fast region-based convolutional network for spectrum interference detection. The proposed model achieves 97.68% accuracy and an F1 score of 96.86% in intrusion traffic detection, with AUC values above 95% for various network attacks. For single-tone interference, it attains 98.65% accuracy, 96.21% recall, and 93.14% precision, converging within 200 iterations with an average recognition accuracy of 95.47%. These results confirm the model’s ability to detect adversarial threats and interference, enhancing satellite communication security.

The wires and ground wires on transmission towers cannot be straight lines, but present different sizes of arcs, which directly affect the safety and transmission quality of the line. In response to this, a research proposes an online monitoring system for transmission towers based on computer video algorithms. The system collects environment and mechanism parameters of transmission lines by installing sensors on transmission towers, monitors them through computer video algorithms, and combines grey wolf algorithm and deep learning models to predict sag, thereby achieving crisis warning of the power grid around transmission towers. The outcomes denoted that during the field testing process, the warning accuracy of the system reaches over 98.57%, and the response time is only 0.5 seconds. The false negative rate and false positive rates are 2% and 0.5%, respectively. Based on the above content, it can be concluded that the proposed online monitoring system for transmission towers can effectively achieve line anomaly warning and maintain stable line operation.

The study analyzes the stylistic evolution of contemporary Chinese literary works using the MONK project. Text mining tools in the project are used to analyze the thematic classification, emotional tendency and stylistic type changes of the works. Among them, LDA model and GBDT algorithm are used to identify the thematic classification of Chinese modern and contemporary literary works, SO-PMI algorithm is used to identify the emotional tendency in the works, and the vector space model can classify the style of the works. Based on the above methods, the theme and emotional changes of modern and contemporary Chinese literary works can be categorized into 3 stages: the awakening of Enlightenmentism at the beginning of the 20th century, the diversified presentation during the revolutionary period, and the diversified development after the reform and opening up. The styles of modern and contemporary Chinese literary works can be divided into epic style, lyrical style, rural theme style and intellectual theme style.

Forecasting the volatility of the stock market price is indispensable for managing the risks associated with market dynamics and provides valuable insights for financial decision in trading strategies. This study aims to enhance the accuracy of volatility prediction for stock market price using hybrid models combining econometric and deep learning approaches. Specifically, it introduces a novel GARCH-CNN-LSTM hybrid model for more precise volatility forecasting of stock market price. The GARCH model is efficient at capturing volatility clusters and kurtosis features, while the CNN excels in extracting spatial patterns from time series data, and LSTM effectively preserves essential information over extended periods. GARCH(1,1) model is selected based on AIC, maximum log-likelihood, and parameter significance. Subsequently, CNN and LSTM models are chosen for their complementary capabilities in volatility prediction. We evaluated the forecasting performance of the hybrid models from out-sample test data, employing Mean Square Error, Root Mean Square Error and Mean Absolute Error. The result indicates that the new model outperforms the existing models with an improvement of 8% to 13% accuracy. Furthermore, we conduct the Diebold-Mariano test to confirm significant differences in performance.

The study constructs a solar cell simulation model and tracks the maximum power output from the solar cell using the MPPT algorithm. Simulation simulation experiments are conducted to analyze the effects of changes in environmental factors such as season, weather, light, temperature, wind speed, etc. on the current and power output of solar cells. The total output power and the peak output power of the solar cell are the largest in summer, which are 7407.69kW and 114.93kW, respectively, and the total output power and the peak output power of the solar cell are the smallest in fall, which are 1748.96kW and 31.58kW, respectively. The peak power output of the solar cell is the largest in sunny days, which is 107.56kW, and the smallest in rainy days, which is 37.06kW. The total solar cell power output is maximum (7896.93kW) on clear to cloudy days and minimum (1955.27kW) on rainy days. The solar cell output current and maximum power values decreased with decreasing light intensity. The ambient temperature has little effect on the short circuit current, the output current increases slightly with increasing temperature, the open circuit voltage decreases drastically with increasing temperature and the maximum output power decreases with increasing temperature. The maximum output power of the solar cell increases with increasing wind speed.

The rise of digital humanities reflects a paradigm shift in literary research. This project applies natural language processing to ancient Chinese literature, embedding an attention mechanism into an iterative null convolutional network for named entity recognition. It also integrates the MacBERT pre-training model with a dual-channel structure of aspectual word and semantic features, designing a hierarchical attention mechanism for aspect-level sentiment analysis. Experimental results show improved recognition and sentiment analysis performance, with evaluation scores exceeding 83%. In Ming Dynasty fiction, craftsmen (44.7%) and merchants (22.4%) were the most frequent characters, highlighting the rise of a commercial economy and civic class. In Tang Dynasty poetry, 67.9% of sentiments were positive, with themes of national honor (0.334) and send-off emotions (0.226) commonly linked, reflecting the era’s prosperity and literary aspirations.

The family of graphs of reduced words of a certain sub-collection of permutations in the union \(\cup_{n\geq 4}\frak{S}_{n}\) of symmetric groups is investigated. The sub-collection is characterised by the hook cycle type \((n-2,1,1)\) with consecutive fixed points. A closed formula for counting the vertices of each member of the family is given and the vertex-degree polynomials for the graphs with their generating series is realised. Some isomorphisms of these graphs with various combinatorial objects are established. Lastly, a link with the Poincar\’e polynomial of the integral cohomology ring of the Grassmannian \({\rm Gr}(2,n)\) is also given.

In this paper, we introduce the concept of the Over-inversion number, which counts the overlined permutations of length \(n\) with \(k\) inversions, allowing the first elements associated with the inversions to be independently overlined or not. We explore its properties and combinatorial interpretations through lattice paths, overpartitions, and tilings, and provide a combinatorial proof demonstrating that these numbers form a log-concave and unimodal sequence.