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Under the new media environment, while enjoying the convenience brought by the propagation of public opinion information (referred to as public opinion), learning the evolution process of public opinion and strengthening the governance of the spreading of public opinion are of great significance to promoting economic development and maintaining social stability as well as effectively resisting the negative impact of its propagation.

Thinking about the results of empirical research and bibliometric analysis, this paper focused on introducing key factors such as information content, social strengthening effects, etc., from both internal and external levels, dynamically designed public opinion spreading rules and netizens' state transition probability. Subsequently, simulation experiments were conducted to discuss the spreading law of public opinion in two types of online social networks and to identify the key factors which influencing its evolution process. Based on the experimental results, the governance strategies for the propagation of negative public opinion were proposed finally.

The results show that compared with other factors, the propagation of public opinion depends more on the attributes of the information content itself. For the propagation of negative public opinion, on the one hand, the regulators should adopt flexible guidance strategy to establish a public opinion supervision mechanism and autonomous system with universal participation. On the other hand, they still need to adopt rigid governance strategy, focusing on the governance timing and netizens with higher network status to forestall the wide-diffusion of public opinion.

The research conclusions put forward the enlightenment for the governance of public opinion in management practice, and also provided decision-making reference for the regulators to reasonably respond to the propagation of public opinion.

Our research proposed a research framework for the discussion of public opinion propagation process and had important practical guiding significance for the governance of public opinion propagation.

In modern society, considering the multi-channel of public opinion information (public opinion) propagation and its strong influence on social development, it is necessary to study its propagation law and discuss the intervention strategy in online social networks (OSN).

First, a conceptual model of double-layer OSN was constructed according to their structural characteristics. Then, a cross-network propagation model of public opinion in double-layer OSN was proposed and discussed its spreading characteristics through numerical simulations. Finally, the control strategy of public opinion, especially the timing and intensity of intervention were discussed.

The results show that the double-layer OSN promotes the propagation of public opinion, and the propagation of public opinion in double-layer OSN has the characteristics of that in two single-layer OSN. Compared with the intervention intensity, the regulator should give the priority to the timing of intervention and try to intervene in the early stage of public opinion propagation.

This study may help the regulators to respond to the propagation of public opinion in OSN more actively and reasonably.

This research has a deep comprehension of the cross-network propagation rules of public opinion and manages the propagation of public opinion.

The purpose is to predict the distribution of the residual pretightening force of the bolt group under the action of any initial pretightening force, and to achieve the final residual pretightening force as the target to solve the initial pretightening force value to be applied.

Based on the finite element method and the elastic interaction theory between bolt group, this paper establishes a prediction model for the residual pretightening force distribution of bolt group for one-step pretightening and multi-step pretightening of gasketless flange connection systems. In addition, using the general modeling method given in this paper, the prediction model of residual pretightening force of long plate bolt connection system is established, and compared with reference, which fully proves the effectiveness and universality of the general prediction model of residual pretightening force of bolt group.

The appropriate pretightening sequence, increasing the number of pretightening steps and variable amplitude loading can effectively reduce the influence of elastic interaction and improve the uniformity of residual pretightening force of the bolt group. And the selection of material, number of bolts and connected thickness of bolt connection system also has a great influence on the distribution of residual pretightening force of bolt groups.

The general prediction model for the residual pretightening force of bolt group of connecting structural components considering elastic interaction given in this paper can provide a reference for the design and optimization of the bolt assembly process of the rotor system and the casing system in aero-engine and the prediction of the performance of the connecting system.