With the growth of the new energy sector, China’s energy industry is experiencing significant transformations. This research aims to evaluate the technological progress and changes in scale efficiency of listed companies in China’s energy industry, with a particular focus on the comparison between new and traditional energy sectors. This research investigates various efficiency values, types of returns to scale, the role of patents in fostering technological progress, and the influence of financial leverage on scale efficiency changes, a comprehensive evaluation of the industry that offers a critical foundation for formulating targeted strategies. This research uses data from A-share listed energy companies spanning from 2017 to 2023, constructs input–output indicators centered on research and development (R&D) and profitability, and applies the DEA model to examine the operating efficiency of energy listed companies. A Malmquist indices is developed to analyze the dynamic evolution of technological change and scale efficiency change. In contrast to the conventional approach of using DEA efficiency scores as the dependent variable in Tobit regressions, this research uses the Malmquist indices, which more effectively captures the dynamic evolution of technological progress and scale efficiency. The study empirically assesses the impact of patent accumulation on technological progress through a Tobit panel model with random effects and the effect of financial leverage on scale efficiency changes using a Tobit four-stage incremental regression. Finally, the study draws the following conclusions: 1. In terms of industry static correlation, listed new energy companies exhibit polarization in returns to scale types; in contrast, traditional energy listed companies have a more stable and mature returns to scale structure. 2. In terms of dynamic correlation, technological progress in the new energy sector is substantial, while the traditional energy sector faces bottlenecks; efficiency changes in both industries are dependent on scale efficiency changes, rather than pure efficiency changes. 3. Regarding influencing factors for new energy listed companies, patent accumulation has a limited impact on technological progress, while financial leverage and scale efficiency change exhibit a non-linear relationship, with an inflection point effect observed in companies with high financial leverage. Finally, this study offers targeted policy recommendations for new energy and traditional energy listed companies based on the findings.

Historically, infectious diseases have greatly impacted human health, necessitating a robust understanding of their trends, processes, and transmission. This study focuses on the COVID-19 pandemic, employing mathematical, statistical, and machine-learning methods to examine its time-series data. We quantify data irregularity using approximate entropy, revealing higher volatility in the U.S., Italy, and India compared to China. We employ the Dynamic Time Warping algorithm to assess regional similarity, finding a strong correlation between the U.S. and Italy. The Seasonal Trend Decomposition using the LOESS algorithm illuminates strong trend degrees in all observed regions, but China's prevention measures show marked effectiveness. These tools, whilst already valuable, still present opportunities for development in both theory and practice.

Existing research on the vulnerability of knowledge innovation networks (KINs) primarily falls into two categories: random attacks and deliberate attacks. This study introduces a novel centrality-based attack framework for the deliberate attack group and systematically examines the impact of different attack mechanisms (such as loss of connectivity, propagation delays, and structural fragmentation) on KINs. Using SCI/SSCI co-authorship data across 286 Chinese cities, this research evaluated network resilience through six key metrics, average clustering coefficient, average degree, average path length, global efficiency, isolated nodes ratio, and largest connected component ratio, thus revealing three key conclusions: First, network density and regional integration surged after 2015, peaking in localized clustering during 2021–2022; yet, post-2022, structural fragmentation and efficiency declines exposed critical vulnerabilities. Second, network disruption simulations revealed that attacks based on structural fragmentation mechanisms have the most significant impact, demonstrating the need to promote polycentric development to reduce core dependency risks and highlighting the importance of protecting high-centrality nodes such as Beijing, Shanghai, and Shenzhen. Third, the inhibitory effect of economic proximity weakened significantly by 2024, suggesting reduced economic disparity barriers to collaboration. Notably, emerging synergies between geographic and economic proximity enhanced innovation cooperation potential, emphasizing spatial–economic coordination as a crucial factor in development-stage planning. By integrating spatiotemporal dynamics with attack taxonomy, our framework advances network theory and equips policymakers with actionable strategies to optimize knowledge flows and mitigate systemic risks. Bridging structural resilience with innovation-driven development, this study offers new insights into China’s urban knowledge networks.

Based on the connotation and goals of high-quality development, a comprehensive evaluation index system, including 19 indicators, is constructed. After processing the data and calculating the index weights, the broad index and sub-indices of the high-quality economic development of Jianyang City are obtained. Research shows that the overall quality of Jianyang’s economic growth is at an acceptable level, but the internal economic development is not balanced. The green ecological index and the people’s livelihood sharing index are significantly higher than the benefits efficiency index, structural optimization index and kinetic energy conversion index.

Addressing the urgent demand for time series prediction in smart manufacturing driven by industrial big data, this paper proposes a convolutional neural networks (CNN)-Transformer hybrid intelligent prediction framework aimed at resolving core issues such as insufficient prediction accuracy and limited model generalization capability caused by high-dimensional, high-noise, and non-stationary data. The framework employs a CNN front-end to extract local temporal features and multi-scale patterns from vibration signals, which are then fed into a Transformer encoder to model global long-term dependencies, achieving effective synergy between local perception and global context. To further enhance the model’s adaptability to practical variable operating conditions, we developed the CNN-Transformer-DA (Domain-Adaptive) enhanced variant, which integrates channel attention, bidirectional temporal modeling, and multi-kernel domain adaptation techniques. Experiments on two bearing datasets, XJTU-SY and PHM2012, demonstrate that the hybrid model significantly outperforms single Gated recurrent unit, Inverted Transformer (iTransformer), and KNN models in remaining useful life prediction, with R ² values reaching 0.918 and 0.982, respectively. CNN-Transformer-DA exhibits excellent performance in cross-condition prediction tasks, achieving an average R ² > 0.86 across three cross-condition tasks on the XJTU-SY dataset, proving its effectiveness in addressing the challenges posed by condition variations. The model achieves optimal performance across all error metrics. These results confirm its comprehensive advantage in capturing degradation trends and local dynamics. This study provides a high-precision, robust fusion modeling approach for predictive maintenance of industrial equipment, holding significant theoretical and practical value.

In this paper, we propose a user-friendly integral inequality to study the coupled parabolic chemotaxis system with singular sensitivity under the Neumann boundary condition. Under a low diffusion rate, the classical solution of this system is uniformly bounded. Our proof replies on the construction of the energy functional containing ${\int }_{\mathsf{\Omega }}\frac{{\left|v\right|}^4}{v^2}$ with $v>0$. It is noteworthy that the inequality used in the paper may be applied to study other chemotaxis systems.