Fiscal decentralization, as a policy with which to regulate the financial power relationships between central and local governments, undoubtedly has an impact on high-quality economic development, and in the current context of focusing on environmental quality its path may include environmental regulation, which is restricted by the degree of decentralization and directly affects high-quality economic development. Based on data from 30 Chinese provinces from 2010 to 2019, this paper empirically tests the moderating effect of environmental regulation on the relationship between fiscal decentralization and high-quality economic development through the use of an intermediary-effect model, a threshold model, and a quantile regression model. The following are the main conclusions: First, fiscal decentralization encourages high-quality economic development with a coefficient of 0.069, but environmental regulation dampens this effect, with a coefficient value of 0.0055 for the suppression effect; after removing endogenous effects, the conclusion remains valid. Second, the influence of fiscal decentralization has different manifestations under different environmental regulation intensities and different levels of high-quality economic development: fiscal decentralization has a larger regression coefficient when the intensity of environmental regulation exceeds 0.0108; it only shows a positive effect in regions with a higher quality of economic development (after the 25% quantile). The main contribution of this paper is the discussion of the impact of fiscal decentralization on high-quality economic development from the perspective of environmental regulation and revealing of a new path for fiscal decentralization to play its role, which is of certain significance in exploring the appropriate degree of decentralization and formulating environmental regulation policies.

Accelerating the development of the digital economy is the way to build a modern industrial system and promote sustainable development. In order to accurately analyze the development status of China’s digital economy, this study introduced a text analysis method to construct an index of the digital economy and surveyed the digital economy based on the panel data of 278 Chinese cities from 2011 to 2019. Moran’s I index, the Dagum Gini coefficient, the kernel density and a Markov chain were used to reveal the space-time difference and dynamic change characteristics. Considering the impact of the spatial correlation and regional division on convergence, we compared the σ values and spatial σ values to study the convergence characteristics after grouping with the decision tree method. The research showed that the digital economy had greatly improved, but it showed a significant imbalance. The research on the regional division of cities according to their geographical distribution and grade showed that the development status of the digital economy was increasingly different, and there was no convergence feature. We chose continuous classification variables and used the decision tree method to divide cities into 10 groups to investigate the convergence. The results showed that the σ values and spatial σ values decreased significantly and showed convergence characteristics. The development of the digital economy showed convergence, indicating that the convergence was greatly affected by the geographical location and grouping basis. Overall, this study contributes to our understanding of the development status of the digital economy, and targeted policy recommendations were proposed to improve the level of digital economy development.

Against the backdrop of the coordinated development of the digital economy and green transformation, the mechanism through which enterprises’ digital transformation affects new quality productive forces deserves systematic examination. Using panel data of Chinese A-share manufacturing listed firms from 2015 to 2023, this paper constructs a two-way fixed effects model and employs an instrumental variable approach to empirically examine the nonlinear impact of digital transformation on new quality productive forces and its underlying mechanisms. From the perspectives of three aspects—nonlinear effects, dual mediation mechanisms, and heterogeneity analysis—this paper systematically uncovers the internal logic through which digital transformation drives new quality productive forces, providing theoretical foundations and policy implications for promoting the coordinated digital and green transformation of the manufacturing sector. It should be noted that this paper has certain limitations. First, the sample is confined to Chinese A-share manufacturing listed firms, and the applicability of the findings to small and medium-sized enterprises and other industries requires further verification. Second, this paper does not fully capture the dynamic evolution of the impact of digital transformation on new quality productive forces. Future research may further deepen the analysis by expanding the sample scope, refining variable measurement, and incorporating dynamic modeling approaches.

In this paper, we study the D- and A-optimal assignment problems for regression models with experimental cost constraints. To solve these two problems, we propose two multiplicative algorithms for obtaining optimal designs and establishing extended D-optimal ($ED$-optimal) and A-optimal ($EA$-optimal) criteria. In addition, we give proof of the convergence of the $ED$-optimal algorithm and draw conjectures about some properties of the $EA$-optimal algorithm. Compared with the classical D- and A-optimal algorithms, the $ED$- and $EA$-optimal algorithms consider not only the accuracy of parameter estimation, but also the experimental cost constraint. The proposed methods work well in the digital example.

To address the limitations of traditional binary option pricing models in capturing the long-range dependence characteristics of financial time series and in neglecting the cognitive fuzziness of parameters, this paper proposes an innovative pricing model that integrates mixed fractional Brownian motion with triangular fuzzy numbers. Mixed fractional Brownian motion is employed to characterize the long-range dependence of stock prices, while triangular fuzzy numbers are used to describe the fuzziness inherent in stock prices and volatility. Based on this framework, a fuzzy pricing model is constructed, and explicit expressions for the price cutsets are derived. Theoretical analysis and numerical experiments show that the influence of the Hurst exponent on option prices is modulated by the exercise time. Empirical results reveal that the underlying asset price exhibits significant long-range dependence, supporting the use of mixed fractional Brownian motion for modeling. Compared with the Black–Scholes model, the fuzzy price interval from the proposed framework covers 98.00% of actual price observations, while the Black–Scholes-based interval covers 84.00%. The interval is also narrower, indicating higher efficiency in uncertainty representation.