An \( (n,r) \)-arc in \( \operatorname{PG}(2,q) \) is a set \( \mathcal{B} \) of points in \( \operatorname{PG}(2,q) \) such that each line in \( \operatorname{PG}(2,q) \) contains at most \( r \) elements of \( \mathcal{B} \) and such that there is at least one line containing exactly \( r \) elements of \( \mathcal{B} \). The value \( m_r(2,q) \) denotes the maximal number \( n \) of points in the projective geometry \( \operatorname{PG}(2,q) \) for which an \( (n,r) \)-arc exists. We show by systematically excluding possible automorphisms that putative \( (44,5) \)-arcs, \( (90,9) \)-arcs in \( \operatorname{PG}(2,11) \), and \( (39,4) \)-arcs in \( \operatorname{PG}(2,13) \)—in case of their existence—are rigid, i.e. they all would only admit the trivial automorphism group of order \( 1 \). In addition, putative \( (50,5) \)-arcs, \( (65,6) \)-arcs, \( (119,10) \)-arcs, \( (133,11) \)-arcs, and \( (146,12) \)-arcs in \( \operatorname{PG}(2,13) \) would be rigid or would admit a unique automorphism group (up to conjugation) of order \( 2 \).

Let \( S \) be a connected union of finitely many \( d \)-dimensional boxes in \( \mathbb{R}^d \) and let \( \mathcal{B} \) represent the family of boxes determined by facet hyperplanes for \( S \), with \( \mathcal{F} \) the associated family of faces (including members of \( \mathcal{B} \)). For set \( F \) in \( \mathcal{F} \), point \( x \) relatively interior to \( F \), and point \( y \) in \( S \), \( x \) sees \( y \) via staircase paths in \( S \) if and only if every point of \( F \) sees \( y \) via such paths. Thus the visibility set of \( x \) is a union of members of \( \mathcal{F} \), as is the staircase kernel of \( S \). A similar result holds for \( k \)-staircase paths in \( S \) and the \( k \)-staircase kernel of \( S \).

The minimum dominating set problem asks for a dominating set with minimum size. First, we determine some vertices contained in the minimum dominating set of a graph. By applying a particular scheme, we ensure that the resulting graph is 2-connected and the length of each formed induced cycle is 0 mod 3. We label every three vertices in the induced cycles of length 0 mod 3. Then there is a way of labeling in which the set of all labeled vertices is the minimum dominating set of the resulting graph, and is contained in the minimum dominating set of the original graph. We also consider the remaining vertices of the minimum dominating set of the original graph and determine all vertices contained in the minimum dominating set of a graph with maximum degree 3. The complexity of the minimum dominating set problem for cubic graphs was shown to be APX-complete in 2000 and this problem is solved by our arguments in polynomial time.

In this paper we study a new graph parameter, the stacking number. Defined in relation to the eternal domination game, we show that there are highly connected graphs for which it is beneficial to allow multiple guards to occupy a vertex, answering an open question of Finbow et al. In fact, we show that for any sequence \( (s_i) \), allowing \( s_j \) guards to occupy a vertex can save arbitrarily many guards in comparison to allowing fewer than this on a vertex. We also show that the stacking number is \( 1 \) for all trees.

The body language of dancers is vital for conveying emotion. In this study, Kinect is used to detect and track dancers’ movements, and we develop two models: a dance action recognition model based on skeleton data and a dance emotion recognition model using an Attention-ConvLSTM. The action recognition model achieves 88.34% accuracy—reaching its best performance after just 40 iterations—while the emotion recognition model reaches an accuracy of 98.95%. Our analysis shows that features such as eigenvalue speed, skeleton pair distance, and inclination effectively differentiate emotions, although certain emotions (e.g., Excited vs. Pleased and Relaxed vs. Sad) can be confused. Notably, the leg’s skeletal points significantly influence emotion expression. Ultimately, the study establishes a dance emotion expression mechanism through coordinated movement changes of the head, hands, legs, waist, and torso.

Deep learning-based target detection algorithms outperform traditional methods by eliminating the need for manual feature design and improving accuracy and efficiency. This paper constructs a YOLOv5 target detection model using a deep convolutional neural network. To enhance accuracy, generalization, and detection speed, three data augmentation techniques—mosaic data enhancement, adaptive anchor frame, and adaptive image scaling—are applied. The model is further optimized with an attention mechanism and a modified YOLOv5 framework. A loss function and global average pooling enhance feature mapping for a fully convolutional network. Experimental results show that the improved YOLOv5n model achieves a 2.9979 percentage point increase in MAP, a 31% improvement in FPS, and a training time reduction of 10 minutes, completing 100 rounds in 20 minutes.

Metacognition, as a fundamental ability for learners to adapt to complex environments, is equally adapted to constructivist teaching and learning activities. In this paper, we propose a model of learning environment characteristics for metacognitive regulation under constructivist learning theory, and utilize Item2Vec algorithm, Self-Attention mechanism, and BiGRU model to construct a model of metacognitive ability. The model presents a kind of multi-channel network characteristic composed of Self-Attention mechanism and BiGRU model. Design a theoretical model of the learning environment oriented to improving students’ metacognitive ability, and analyze the functional modules of the overall system of the learning environment. Propose a learning activity aiming at the improvement of metacognitive ability and incorporating constructivist theory as the guiding concept to allocate the various aspects of the whole constructivist teaching activity. Analyze the implementation effect of constructivist teaching activities based on metacognitive strategies and organize the influencing factors of metacognitive strategies. The bivariate correlation analysis of students’ total test scores and usual grades are closely related to planning strategies, monitoring strategies, and regulating strategies, and the significance (two-tailed) is less than 0.01. This indicates that the higher the students’ scores, the higher the corresponding level of metacognitive strategies.

Civil engineering crack detection faces challenges due to complex environments and external interferences. This paper proposes an improved YOLO v8s-WOMA network, integrating ODConv, C2f-MA modules, and WIoU loss function to enhance crack identification accuracy. A BP neural network is also trained to assess crack damage. Experiments on the CBP dataset compare this method with existing detection algorithms. Results show that the proposed model achieves the highest mAP (90.5%), F1-score (90.3%), and accuracy (89.6%). Bridge crack detection errors remain within 0.1mm (width) and 20mm (length), ensuring precise damage assessment. The model effectively handles complex backgrounds, accurately detects cracks, and meets practical engineering needs.

The rapid growth of multilingual information online has made traditional translation insufficient, highlighting the need for intelligent language translation. This study employs a convolutional neural network to extract visual features from translated images and uses region-selective attention to align text and image features. The fused information is then processed through a sequence model to develop a computer vision-based translation algorithm. Results show that the proposed algorithm excels in key evaluation metrics, improving translation quality. It maintains a low leakage rate (1.30%), a mistranslation rate of 2.64%, and an average response time of 67.28ms. With strong generalization and applicability in multilingual translation, the algorithm demonstrates high performance and promising real-world applications.

This paper addresses the limitations of the traditional portfolio theory centered on the mean-variance model and expected utility theory, and proposes the establishment of a portfolio model that takes into account the subjective psychological factors of investors, taking into account the fact that investors are susceptible to the influence of various psychological biases, affective biases, and cognitive biases in the actual decision-making process, with respect to the theory of consistency of the assumptions of the investor’s risk attitude. The portfolio model based on fuzzy decision-making is proposed, combined with the development and application of linear programming in portfolio optimization, the return of assets is regarded as a random fuzzy variable, and the stochastic fuzzy portfolio model is constructed to consider the risk characteristics of investors. The portfolio returns under different emotions or different risk preferences are explored separately. Combined with the fund categorization allocation of the sample firms, the fund portfolio C based on the fuzzy portfolio model is proposed and compared with the equal weight allocation fund (fund portfolio A) and the risk coefficient weighted allocation fund (fund portfolio B) based on the risk level of return, respectively. Fund Portfolio C has the highest average return.

Given a prime \( p \), a \( p \)-smooth integer is an integer whose prime factors are all at most \( p \). Let \( S_p \) be the multiplicative subgroup of \( \mathbb{Q} \) generated by \(-1\) and the \( p \)-smooth integers. Define the \( p \)-smooth partial field as \( \mathbb{S}_p = (\mathbb{Q}, S_p) \). Let \( g \) be the golden ratio \( (1+\sqrt{5})/2 \). Let \( G_p \) to be the multiplicative subgroup of \( \mathbb{R} \) generated by \( g \), \(-1\), and the \( p \)-smooth integers. Define the \( p \)-golden partial field as \( \mathbb{G}_p = (\mathbb{R}, G_p) \). The partial field \( \mathbb{S}_2 \) is actually the well-known dyadic partial field and \( \mathbb{S}_3 \) has sometimes been called the Gersonides partial field. We calculate the fundamental elements of \( \mathbb{S}_5 \), \( \mathbb{G}_2 \), \( \mathbb{G}_3 \), and \( \mathbb{G}_5 \).
Our proofs make use of the SageMath computational package.

Let \(P_k\) and \(C_k\) respectively denote a path and a cycle on \(k\) vertices. In this paper, we give necessary and sufficient conditions for the existence of a complete \(\left\{P_7,C_6\right\}\)-decomposition of the cartesian product of complete graphs.

Rural ecological protection and restoration projects are actively underway worldwide, yet in‐depth research on the evolution of rural ecosystems and their underlying mechanisms remains limited. This study investigates the distribution characteristics of rural ecosystems in Ganzhou District by analyzing their number, spatial type, and density. Geodetectors are employed to examine the spatial heterogeneity and key driving factors of these ecosystems. In addition, we assess how the integrated ecosystem service index responds to land use changes, revealing that the proportion of ecological land—contributing up to 50%—is the most significant factor, with grassland showing a strong positive effect (average coefficient 7.99) and construction land exhibiting a negative correlation with the CES index. These findings offer scientific guidance for enhancing rural ecological protection through improved legislation, ecological compensation, and legal aid.

The internal defects and concrete strength detection of concealed mass concrete structures (dams, fan foundations, tunnel arches, etc.) has been a difficult problem in the industry, and there is a lack of effective nondestructive testing technology, conventional single-sided nondestructive testing technology (ground-penetrating radar, ultrasonic array, impact echo method, etc.) in reinforced concrete structures can not be more than 3m in depth, and the practical application is limited. For this reason, we have developed a new face wave CT inspection technique based on elastic wave face wave, combining the excellent wavelength method and multiple filtering method to solve the problem of difficult extraction of frequency dispersion curves of the face wave in concrete, and through finite element simulation and example verification, it is confirmed that the method can detect the defects and strength of the concrete structure on a single side, and the effective detection depth is more than 4m, which has a strong practical application value.

With the advancement of information technology, universities accumulate vast amounts of data, but effectively extracting and utilizing this information remains a challenge. Existing studies on university management data often rely on shallow analysis with basic models and tools, offering limited efficiency improvements. This paper explores an optimized higher education management data analysis algorithm, leveraging artificial intelligence and multimedia technology to enhance efficiency. A comparative study with traditional methods shows that the proposed algorithm improves university management data analysis efficiency by 11.4%.

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.

This paper aims at resolving the issue that the conventional literature study can’t deal with the large amount of data, the author proposes a research method for theme clustering and text mining of Chinese modern and contemporary literary texts in the network era. The author studied how to effectively improve the thematic clustering performance of literary texts based on keyword clustering ensemble method. Comparing two clustering ensemble methods (K-means based data ensemble and incremental clustering based algorithm ensemble) and four keyword extraction methods (TF-ISF CSI, ECC, TextRank), the effects of various keywords on the results of thematic clustering were analysed. Experiments indicate that the clustering algorithm can greatly increase the topic clustering efficiency, and it is more stable when the key words are less. The author’s research provides new technological means for text mining and thematic clustering in contemporary Chinese literature, which helps to promote the development of digital humanities research.

The undifferentiated recommendations in current library management systems fail to meet the diverse and personalized needs of users, and the vast amounts of user data accumulated over the years remain largely untapped. This paper integrates personalized recommendation requirements in self-service libraries with K-means clustering to design a labeling system and set user profile weights. Building on traditional reinforcement learning, we propose an Actor–Critic based recommendation algorithm that models the library recommendation task as a Markov decision process to automatically learn an optimal strategy by maximizing expected long-term rewards. The DDPG algorithm is employed to train the parameters of this framework, achieving improved personalized performance. Comparative experiments on datasets (ML-100k, Yahoo! Music, ML-1M, and Jester) demonstrate that our model outperforms traditional methods and DeepFM, with scores of 0.7708, 0.1918, 0.7155, and 0.3936, respectively. This study provides innovative insights for accurate recommendations and enhanced user experience in libraries.

The application of virtual reality (VR) technology in teaching is increasingly widespread. This study leverages VR to create cross-cultural teaching contexts and develop speech recognition models for language learning. An ecological model of language learning based on VR is constructed, and a cross-cultural contextual VR system is implemented and introduced into language education. Testing reveals that the system achieves a speech recognition efficiency of 99.7% and a correctness rate of 99.5%. Moreover, a comparison of pre- and post-test data between experimental and control groups shows that the experimental group significantly outperformed the control group in English proficiency (p < 0.05). Overall, the cross-cultural contextual VR system demonstrates a significant positive impact on language learning outcomes.

New media advertising boosts platform revenue, and intelligent content optimization enhances its effectiveness. This paper applies a multi-task deep learning neural network to optimize advertisement content, leveraging attention mechanisms and loss functions to improve performance. Blockchain technology is integrated to create a personalized and accurate recommendation system. Experimental results show that the proposed model effectively optimizes ad content, meeting functional and performance requirements. Most users’ ad browsing duration exceeds 50 seconds, outperforming traditional recommendation systems. The proposed system offers strong targeting, fast results, and cost efficiency, significantly enhancing user engagement with ad content.

With the frequent occurrence of global climate change and extreme weather events, meteorological forecasting technology has gradually become an auxiliary technology for production activities. In order to improve the quality of meteorological analysis results, a technology utilizing cloud radar data as the core is proposed. The vertical distribution of water vapor and liquid water in the atmosphere is detected by a ground-based microwave radiometer. The median filtering method is used to further smooth the classified and preliminarily removed reflectance factor data, and computer information processing technology is used for data analysis. The experimental results of Taiyuan ground based remote sensing high altitude detection experiment showed that in the data availability test, the research method had a data availability rate of 97.3% when the height was 2km in humidity data. When conducting accuracy analysis of the results, the root mean square error of the relative humidity profile was only 22.0% when the height increased to 12km. This indicates that the research method can conduct high-quality meteorological analysis and provide assistance for meteorological forecasting.

A \((d, 1)\)-total labelling of a graph \(G\) is an assignment of integers \(\{0,1,\cdots,l\}\) to the vertices and edges of the graph such that adjacent vertices receive distinct integers, adjacent edges receive distinct integers, and the integer received by a vertex differs at least \(d\) from those received by its incident edges. The minimum number \(l\) required for such an assignment is called the \((d, 1)\)-total number of the graph \(G\). This paper contributes to \((d,1)\)-total labelling of two infinite families of snarks, the Goldberg family and the Loupekhine family. We completely determine the \((d,1)\)-total numbers of these two families of snarks for all \(d\geq2\).

A prism fuzzy number is the integration of triangular and trapezoidal fuzzy numbers. In this artifact, the balancing point and the grading value of the prism fuzzy number is defined. By using prism fuzzy number, we were able to infer the Trapezoidal and Triangular fuzzy numbers. A comparative study with the current model is done to corroborate our findings. An enhanced grading technique for evaluating the prism fuzzy numbers is defined. Finally, the application of prism fuzzy numbers to assess student’s interest in higher studies and employment is illustrated using the MATLAB simulation. A statistical analysis is demonstrated using the Python programme with real-life data.

Achieving accurate prediction of financial market fluctuations is beneficial for investors to make decisions, while machine learning algorithms can utilize a large amount of data for training and learning, which has good effect on predicting financial market fluctuations. The article first analyzes the financial dataset, and then constructs a feature selection model by combining Boruta and SHAP to screen the financial data features. Based on the LSTM model, a new Dropout layer and fully connected layer are designed to construct the AMP-LSTM model to realize the prediction of financial market fluctuations. The Boruta SHAP algorithm has a RMSPE of 0.242, which is good for screening. The prediction performance of the AMP-LSTM model is significantly better than that of the traditional LSTM (p<0.01), and the predicted values are closer to the actual values. The method in this paper performs better than MLP, RNN and other methods in general in terms of error performance when predicting indicators such as WTI, Brent, LGO, etc., and is able to realize the prediction of financial market volatility in the digital economy environment.

Aiming to address shortcomings in existing time series prediction models, this paper proposes an LSTM model enhanced by fused multi-scale convolutional attention (MCA-LSTM). We design the experimental parameters, construct a stock price dataset, and model the improved LSTM using individual stock closing prices, with prediction accuracy evaluated via RMSE, MAPE, and MAD. To assess the arbitrage and generalization performance of the MCA-LSTM portfolio model, we compare the application of the MCA-LSTM-BL model. Furthermore, within the framework of a mean semi-absolute deviation (MSAD) portfolio optimization model, we develop a new portfolio optimization approach based on return forecasting (MCA-LSTM+MSAD). The asset values and return predictions of various portfolio models are analyzed under transaction cost considerations, and the proposed MCA-LSTM+MSAD model achieves an excess return of 56.98%, consistently maintaining the highest portfolio value throughout the trading period. Overall, our findings indicate that the MCA-LSTM+MSAD model is a promising tool for portfolio optimization and warrants further development for real investment applications.

In this paper, we prove that, the Wiener index of a connected tripartite graph is any natural number except 1, 2, 5, 6 and 11.

For every connected graph \(F\) with \(n\) vertices and every graph \(G\) with chromatic surplus \(s(G)\leq n\), the Ramsey number \(r(F,G)\) satisfies \(
r(F,G) \geq (n-1)(\chi(G)-1) + s(G), \) where \(\chi(G)\) denotes the chromatic number of \(G\). If this lower bound is attained, then \(F\) is called \(G\)-good. For all connected graphs \(G\) with at most six vertices and \(\chi(G) \geq 4\), every tree \(T_n\) of order \(n\geq 5\) is \(G\)-good. In case of \(\chi(G) = 3\) and \(G \neq K_6-3K_2\), every non-star tree \(T_n\) is \(G\)-good except for some small \(n\), whereas \(r(S_n,G)\) for the star \(S_n = K_{1,n-1}\) in a few cases differs by at most 2 from the lower bound. In this note, we prove that the values of \(r(S_n,K_6-3K_2)\) are considerably larger for sufficiently large \(n\). Furthermore, exact values of \(r(S_n,K_6-3K_2)\) are obtained for small \(n\).

Let \(A\) be a real algebra. It is called locally complex algebra if every non-zero element generates a subalgebra isomorphic to either \(\mathbb{R}\) or \(\mathbb{C}.\) It is said to satisfy the  uniqueness of the square root except the sign if the equation \(x^2=y^2\) implies \(y=\pm x.\) We show the following:
1. Every locally complex algebra is a quadratic algebra.
2. Every alternative locally complex algebra is isomorphic to either \(\mathbb{R},\) \(\mathbb{C},\) \(\mathbb{H}\) or \(\mathbb{O}.\)
3. Every commutative locally complex algebra without divisors of zero is isomorphic to \(\mathbb{R}\) or \(\mathbb{C}.\)
4. Every finite-dimensional algebra satisfying the uniqueness of the square root except the sign has dimension \(\leq 2\) and contains non-zero idempotents.

To solve the problem of identifying intrinsic relationships between objects and mirror segmentation in semantic segmentation of urban scenes using current multi-modal data, this study innovatively integrates color images, depth information, and thermal images to propose a network model that integrates modal memory sharing and form complementarity, and a hierarchical assisted fusion network model. Compared with existing advanced urban scene semantic segmentation methods, the proposed method performed excellently in terms of performance, with an average pixel accuracy and mean intersection over union of over 80% for different objects. In addition, the research method achieved clearer and more complete segmentation results by strengthening contextual associations, and edge processing is also smoother. Even in object segmentation with similarities in distance, shape, and brightness such as “vegetation” and “sidewalk”, the research method still maintained high accuracy. The research method can effectively handle the complexity of urban scenes, providing a new solution for semantic segmentation of multi-modal data in urban scenes.

Blockchain technology has the characteristics of data anti-tampering and anti-forgery, which can provide solution ideas for the secure storage and transmission of data in distributed networks. The study applies blockchain technology to data auditing, constructs an aggregated signature based on conditional identity anonymization to protect user privacy, simplifies the auditing computation by using homomorphic hash function, and deploys three kinds of smart contracts on the blockchain to design a blockchain-based data integrity auditing scheme. For the privacy protection problem, a blockchain privacy protection model based on differential privacy is constructed by integrating the differential privacy policy into the blockchain smart contract layer. The experimental results show that the data integrity auditing scheme has superior blockchain storage cost and time overhead, and the average time overhead under different dynamic operations is below 30ms. The privacy protection model also exhibits high efficiency, with encryption and decryption times of 0.075s and 0.063s, respectively, under the largest data file, and a significant speed advantage in all phases of operation. The proposed scheme in this paper meets the needs of data integrity and privacy protection, and can provide efficient services for users.

Mango weaving, a traditional handicraft in Guangxi, is facing decline. This study explores AI technology’s role in its protection and innovation by analyzing consumer reviews using perceived value theory and the LDA topic model to identify preferences for improving production. A lightweight generative adversarial network with a non-local attention mechanism is proposed for text-to-multi-objective image generation, aiding innovative design. Consumers expressed 82.6% satisfaction with mango weaving. Reviews were categorized into five themes, highlighting the need for improvements in emotion, quality, and price. The AI-generated image model outperformed others, with IS and FID scores improving by 21.85% and 16.46%, respectively. AI enhances mango weaving by refining design, improving product quality, and expanding its preservation and development.

The ocean is vital for human survival and development, serving as the birthplace of life and a source of food, minerals, and scientific research materials. It plays a crucial role in global trade, economic growth, climate regulation, and ecological balance. Underwater positioning technology is fundamental to marine engineering, with underwater acoustic passive positioning being essential for sonar source localization. Active and passive acoustic systems help measure underwater noise and determine target locations. Passive systems rely on signals emitted by targets, while active systems use interaction signals for positioning. This study applies machine learning to improve acoustic beacon signal recognition in underwater positioning. Results show that machine learning enhances recognition speed by 8% and detection accuracy by 9% compared to traditional methods. By optimizing underwater acoustic signal recognition, this approach enhances positioning accuracy, reduces costs, and advances intelligent marine technology, providing innovative solutions for complex marine environments.

Nowadays, “Artificial Intelligence + Education” is transforming teaching and learning. In this study, we employ AI-based data mining to innovate educational management by designing an academic monitoring system using K-means clustering and developing an early warning model through stacking multi-model superposition. Targeted management measures, including personalized video recommendations, are implemented based on the model’s predictions to promote individualized student development. By analyzing daily behavior data from 500 college students, the K-means algorithm effectively classified them into four groups, and the academic alert model achieved a prediction accuracy of 84.19%, outperforming single base models. The implementation of this personalized management method significantly improved student performance compared to traditional approaches, demonstrating its potential to enhance educational outcomes.

Let \( p \) be a prime number, and let \( k \) and \( m \) be positive integers with \( k \geq 2 \). This paper studies the algebraic structure of \(\lambda\)-constacyclic codes of arbitrary length over the finite commutative ring \( R = \frac{\mathbb{F}_{p^m}[u, v]}{ \langle u^k, v^2, uv – vu \rangle } \), where \(\lambda\) is a unit in \( R \) given by \( \lambda = \sum\limits_{i=0}^{k-1} \lambda_i u^i + v\sum\limits_{i=0}^{k-1} \lambda_i’ u^i \), with \(\lambda_i, \lambda_i’ \in \mathbb{F}_{p^m}\) and \(\lambda_0, \lambda_1 \neq 0\). We provide a complete classification of these constacyclic codes, determine their dual structures, and compute their Hamming distances when the code length is \( p^s \).

In this paper, the hyperoctahedral group algebra \(\mathscr{F}[\overrightarrow{S_{n}}]\) over a splitting field \(\mathscr{F}\) of wreath product \(\overrightarrow{S_{n}}\) with \(\text{char}(\mathscr{F})\nmid|\overrightarrow{S_{n}}|\), is considered and the unique idempotents corresponding to the four linear characters of the group \(\overrightarrow{S_{n}}\) are explored. Also, by establishing the minimum weights and dimensions, all group codes generated by the linear idempotents in the aforementioned group algebra are completely characterized for every \(n\). The nonlinear idempotents corresponding to nonlinear characters of \(\overrightarrow{S_{3}}\) are also obtained and various group codes in \(\mathscr{F}[\overrightarrow{S_{3}}]\) generated by linear and nonlinear idempotents are examined.

Let \( G = (V, E) \) be a graph with minimum degree at least one. The general inverse degree of \( G \) is defined as \(\sum\limits_{v \in V} \frac{1}{d^{\alpha}(v)}\), where \( \alpha \) is a real number with \( \alpha > 0 \). In this paper, we present sufficient conditions involving the general inverse degree with \( \alpha \geq 1 \) for some Hamiltonian properties of graphs and upper bounds for the general inverse degree with \( \alpha \geq 1 \).

In today’s era, the rapid development of artificial intelligence is transforming warehousing and logistics by enhancing efficiency and reducing labor costs. In this paper, we first employ a least squares support vector machine to develop an inventory prediction model for warehousing logistics, accurately forecasting inventory values. Next, we design an automated logistics and warehousing architecture that facilitates seamless data transfer and information feedback. Finally, this architecture is used to build a comprehensive inventory management model. Our analysis shows that the AI-based prediction nearly matches the actual inventory value (229 vs. 230) and achieves an inventory turnover rate of 5 times per month, which significantly reduces backlog and improves overall management efficiency and user satisfaction.

The Cascaded Integrator Comb (CIC) decimation filter is a pivotal technology extensively employed in digital signal processing (DSP). This paper delves into a comprehensive examination of the CIC algorithm within software-defined radio (SDR) systems from the perspective of parallel computing and introduces a novel Non-Recursive Implementation (NR-I) on an NVIDIA GPU using CUDA. The NR-I approach significantly reduces computational load by unfolding the recursive CIC structure with pre-derived Unfold Factors. Further optimization was achieved through data-transfer enhancements using PM Implementation (PM-I) and ODT Implementation (ODT-I). Experimental results demonstrate that NR-I achieves a speedup of over 449.48. Additionally, the data-transfer optimizations resulted in substantial performance improvements, with PM-I and ODT-I reducing execution time by 43.24% and 64.22%, respectively. The GPU implementation’s speedup is significantly greater than that of OpenMP, ranging from 3.34 to 10.22 times. These results underscore the effectiveness of the proposed Non-Recursive Implementation in accelerating time-intensive and data-intensive computations.

This paper presents a new sequence called the \(k-\)division sequence. The Pell and Lehmer sequences are then used to define new sequences called the \(k-\)division \(L-\)Lehmer-Pell sequences and some properties of these sequences are determined. Then the \(k-\)division \(L-\)Lehmer-Pell sequences and corresponding self-invertible matrices are used in a new Affine-Hill cipher algorithm. The security of this cipher is examined.

In the era of globalization and intense market competition, strategic human resource management (SHRM) is critical for boosting corporate competitiveness. This study employs structural equation modeling (SEM) and multiple linear regression to uncover the complex influence of SHRM perceptions on employee proactive behaviors, and uses a convolutional neural network (CNN) to explore nonlinear relationships and validate the SEM findings. Results reveal that SHRM perception has a significant positive effect on employee proactive behavior (\(\beta = 0.254\), \(p<0.001\)). Mediators such as job self-efficacy and conceptual psychological contract play a positive role, with indirect effects of 0.1043 and 0.1726, respectively, while insider identity perception significantly moderates the relationship (\(\beta = 0.09\), \(p<0.01\)). The CNN model ranks the importance of variables in descending order as: conceptual psychological contract, job self-efficacy, SHRM perception, job category, and insider identity perception, consistent with the SEM results. These findings highlight the potential of CNNs to optimize HR strategies and enhance employee motivation.

One of the urgent challenges in auditing today is preventing accounting management risk. This study integrates big data auditing technology to enhance audit quality by developing an audit risk assessment index system based on material misstatement risk and inspection risk. By combining the hierarchical analysis and entropy weighting methods to assign risk indicators, the accounting audit risk index for Company Z was calculated using a multi-level fuzzy comprehensive evaluation method and regression analysis to examine impact factors. Empirical evidence shows that the overall expected audit risk is 0.412—indicating a low to average risk level—with significant correlations between the previous year’s audit opinion, audit fee, and other factors such as the largest shareholder’s holding, board size, percentage of independent directors, operating income growth, net profit, and the audit environment. The study focuses on developing effective prevention and response strategies in the era of big data and offers recommendations to reduce potential auditing risks.