The combination of thermal power units’ stability and energy storage systems’ rapid response time enhances power system frequency control. However, high costs and battery life impacts from charging/discharging strategies limit energy storage adoption. This study proposes an adaptive weight-based particle swarm optimization algorithm (APSO) to optimize energy storage control for joint thermal-storage frequency modulation (FM). By analyzing the coupling between state of charge (SOC) and charging/discharging power, the study implements “shallow charging and discharging” with dynamic SOC constraints. The improved PSO algorithm integrates adaptive weighting to overcome local optimal convergence, enhancing global search capabilities and particle migration. Simulation results, based on real-world power plant data, show improved FM accuracy, faster regulation, and reduced energy storage system loss, significantly boosting economic efficiency.

With the increasing penetration of distributed intermittent energy into distribution networks, the self-healing problem of distribution networks faces significant challenges. The load level and demand response must be considered as critical factors affecting fault recovery. This paper proposes a fault recovery strategy that combines islanding division and network reconstruction. First, a distribution network model with a distributed energy storage system is established. To optimize the use of distributed energy resources, controllable loads that can respond to demand are prioritized, and high-priority loads are included in the islanded network after a fault. Based on the islanding division results, the remaining non-faulty power loss areas are restored through main network reconstruction. The improved whale optimization algorithm is employed to solve the problem. Simulation results demonstrate that load demand response is closely linked to the islanding process, and an optimal fault recovery strategy can be achieved by utilizing the distributed energy storage system and the main network.

With the rise of digital technology, global cross-border information flows are driving significant growth in international digital commerce. This paper employs Meta-analysis to examine the impact of cross-border information flows on global trade competitiveness. It outlines the Meta-analysis paradigm, explores the relationship between data element valorization and trade competitiveness, and highlights the varying effects across different stages of the trade process. Using correlation coefficients as effect values, the study transforms and calculates data with the help of formulas and software to comprehensively analyze and test the relationship. The findings reveal rapid growth in China’s digital economy, expanding from 22.6 trillion yuan in 2016 to 51.9 trillion yuan in 2022, deeply influencing industrial structures. In global cross-border data flows, China and Russia exhibit tighter regulations, with China’s DSTRI value rising from 0.325 to 0.347 million USD, demonstrating that cross-border data flows significantly impact global trade competitiveness.

In the era of intelligent education, technology is reshaping traditional music education by enhancing teaching quality, optimizing curriculum design, and improving teacher resources. However, its redistributive effects remain underexplored. This study examines how intelligent education technology impacts resource distribution in music education, focusing on the context of music teacher certification. The research highlights the reform needs of music teacher education, including student-centered goals, improved teaching methods, and optimized curricula. It introduces a music intelligence system based on a radial basis function (RBF) neural network and evaluates its potential in promoting equitable resource distribution through interactive teaching. Findings reveal that intelligent education technology enhances student learning outcomes and music skills by enabling personalized learning paths and strengthening practical teaching. Experimental results confirm the system’s effectiveness in significantly improving students’ music grades, demonstrating its value in transforming music education.

In the modern era, the cultivation of foreign talents extends beyond the traditional enhancement of humanistic knowledge, with literature playing a pivotal role. Addressing the challenges posed by the “golden curriculum,” this study uses the “Selected British and American Stories” program as an example to explore a blended learning and sorting approach. Aligned with the Ministry of Education’s emphasis on “golden subjects,” the research formulates an implementation strategy for curriculum development. In the context of the Ministry’s promotion of the mixed funding program in 2019, the study highlights the necessity of guiding students to utilize the Internet for data-driven blended learning. By emphasizing active engagement, intrinsic motivation, and flexible learning approaches, the proposed strategy aims to enhance teaching quality and align with contemporary educational reform priorities. Furthermore, the paper underscores the significance of equitable teaching evaluation as a feedback mechanism, actively contributing to the overall improvement of teaching quality.

An injective coloring of a given graph \(G = (V, E)\) is a vertex coloring of \(G\) such that any two vertices with a common neighbor receive distinct colors. An \(e\)-injective coloring of a graph \(G\) is a vertex coloring of \(G\) in which any two vertices \(v, u\) with a common edge \(e\) (\(e \neq uv\)) receive distinct colors; in other words, any two end vertices of a path \(P_4\) in \(G\) achieve different colors. With this new definition, we want to take a review of injective coloring of a graph from the new point of view. For this purpose, we review the conjectures raised so far in the literature of injective coloring and \(2\)-distance coloring, from the new approach of \(e\)-injective coloring. Additionally, we prove that, for disjoint graphs \(G, H\), with \(E(G) \neq \emptyset\) and \(E(H) \neq \emptyset\), \(\chi_{ei}(G \cup H) = \max\{\chi_{ei}(G), \chi_{ei}(H)\}\) and \(\chi_{ei}(G \vee H) = |V(G)| + |V(H)|.\) The \(e\)-injective chromatic number of \(G\) versus the maximum degree and packing number of \(G\) is investigated, and we denote \(\max\{\chi_{ei}(G), \chi_{ei}(H)\} \leq \chi_{ei}(G \square H) \leq \chi_{2}(G)\chi_{2}(H).\) Finally, we prove that, for any tree \(T\) (\(T\) is not a star), \(\chi_{ei}(T) = \chi(T),\) and we obtain the exact value of the \(e\)-injective chromatic number for some specified graphs.

In the literature of algebraic graph theory, an algebraic intersection graph called the invariant intersection graph of a graph has been constructed from the automorphism group of a graph. A specific class of these invariant intersection graphs was identified as the \(n\)-inordinate invariant intersection graphs, and its structural properties has been studied. In this article, we study the different types of proper vertex coloring schemes of these \(n\)-inordinate invariant intersection graphs and their complements, by obtaining the coloring pattern and the chromatic number associated.

This paper examines how digital entertainment consumption drives China’s economic growth from multiple dimensions. Using panel data from 260 prefecture-level cities (2020–2022) and a multi-temporal double-difference method, the study finds that digital entertainment consumption significantly promotes economic growth, with a direct effect coefficient of 0.748. Robustness tests via the PSM-DID method confirm this effect, with a coefficient of 0.714, significant at the 5% level. In the low digital divide group, the regression coefficient is 6.325, while it is significantly lower in the high digital divide group, indicating that the digital divide weakens the effect. Heterogeneity analysis shows that enhancing consumer experience, generating new businesses, and boosting cultural influence positively impact growth. The findings provide insights for the sustainable development of the entertainment industry and the digital economy.

Financial frauds, often executed through asset transfers and profit inflation, aim to reduce taxes and secure credits. To enhance the accuracy and efficiency of accounting data auditing, this study proposes an anomaly detection scheme based on a deep autoencoder neural network. Financial statement entries are extracted from the accounting information system, and global and local anomaly features are defined based on the attribute values of normal and fraudulent accounts, corresponding to individual and combined anomaly attribute values. The AE network is trained to identify anomalies using account attribute scores. Results demonstrate classification accuracies of 91.7%, 90.3%, and 90.9% for sample ratios of 8:2, 7:3, and 6:4, respectively. The precision, recall, and F1 score reach 90.85%, 90.77%, and 90.81%, respectively. Training takes 95.81ms, with recognition classification requiring only 0.02ms. The proposed deep neural network achieves high recognition accuracy and speed, significantly improving the detection of financial statement anomalies and fraud.

The core of financial institutions’ big data lies in risk control, making network security threat identification essential for enhancing data processing and service levels. This study applies the principles of network information transmission security prevention, combining frequency domain analysis and distributed processing to extract threat characteristics. A financial network security threat identification model is developed using BiGRU and Transformer models, and a SQLIA defense system is constructed by integrating multi-variant execution and SQL injection attack prevention. Additionally, an intelligent network security defense strategy is formulated based on finite rationality theory. Simulation results show an F1 composite score of 90.78% for threat identification, and the STRIPS-BR defense strategy reduces relative risk by 74.81% during peak times compared to other strategies. Supported by big data, this system ensures secure data transmission and enhances the network service capabilities of financial institutions.