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The purpose of this paper is to extract electrochemical reaction kinetics parameters, such as Tafel slope, exchange current density and equilibrium potential, which cannot be directly measured, this study aims to propose an improved particle swarm optimization (PSO) algorithm.

In traditional PSO algorithms, each particle’s historical optimal solution is compared with the global optimal solution in each iteration step, and the optimal solution is replaced with a certain probability to achieve the goal of jumping out of the local optimum. However, this will to some extent undermine the (true) optimal solution. In view of this, this study has improved the traditional algorithm: at each iteration of each particle, the historical optimal solution is not compared with the global optimal solution. Instead, after all particles have iterated, the optimal solution is selected and compared with the global optimal solution and then the optimal solution is replaced with a certain probability. This to some extent protects the global optimal solution.

The polarization curve plotted by this equation is in good agreement with the experimental values, which demonstrates the reliability of this algorithm and provides a new method for measuring electrochemical parameters.

This study has improved the traditional method, which has high accuracy and can provide great support for corrosion research.

The aim of this study is to discern the role of digital finance in driving rural industrial integration and revitalization. Specifically, it intends to shed light on how the deep development of digital finance can contribute to the optimization and transformation of the rural industrial structure. The research further explores the particular effects of this financial transformation in the central and western regions of China.

This research studies the influence of digital finance on rural industrial integration across 30 Chinese provinces from 2011 to 2020. Utilizing the entropy weight method, a comprehensive evaluation index system is established to gauge the level of rural industrial integration. A two-way fixed effects model, intermediary effect model, and threshold effect model are employed to decipher the relationship between digital finance and rural industrial integration.

Findings reveal a positive relationship between digital finance and rural industrial integration. A single threshold feature was identified: beyond a traditional finance development level, the marginal effect of digital finance on rural industrial integration increases. These effects are more noticeable in central and western regions.

Empirical outcomes contribute to policy discourse on rural digital finance, assisting policymakers in crafting effective strategies. Understanding the threshold of traditional finance development provides a new perspective on the potential of digital finance to drive rural industrial integration.