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The purpose of this study is to empirically examine the cause–effect relationships between workplace friendship and knowledge-sharing behavior, from a static perspective. Furthermore, it investigates the bi-directional relationship between the increase in both workplace friendship and knowledge-sharing behavior over same time periods, and also endeavors to identify whether there is a significant negative lagged effect of the increase in both workplace friendship on knowledge-sharing behavior, and vice versa, across time from a dynamic perspective.

The study conducts a three-wave questionnaire survey to test the research model. A latent change score approach was used to test the direct relationship between changes in workplace friendship and changes in knowledge-sharing behavior.

The findings reveal that knowledge-sharing behavior fosters workplace friendship and workplace friendship promotes the emergence of knowledge-sharing behavior. An increase in workplace friendship promotes an increase in knowledge-sharing behavior over same time periods. However, an increase in workplace friendship will lead to a lagged decrease of knowledge-sharing behavior across time, and vice versa.

The time interval in this study is a little short to capture the full changes in workplace friendship. Some important control factors and mediating mechanisms are not included in the research model.

This study guides managers to focus on various motivators to better strengthen workplace friendship and knowledge-sharing behavior and to consider and effectively respond to the negative side of workplace friendship and knowledge-sharing behavior across time.

This study emphasizes the predictivity of one important interaction patterns, namely, knowledge-sharing behavior on friendship at the workplace, from a static perspective. This study also shows the benefits of an increase in workplace friendship for the development of knowledge-sharing behavior in the same time period. Furthermore, the study presents a counterintuitive finding when taking the lag effect into consideration in exploring the relationship between changes both in workplace friendship and knowledge-sharing behavior, and identifies a negative side of both when viewed over longer periods.

Unlike traditional industries, the e-cigarette is an epoch-making innovative product originating in China and occupying an absolute competitive advantage in the international market. The traditional A-U model describes the laws and characteristics of technological innovation in developed countries. In contrast, the inverse A-U model depicts the process of “secondary innovation” in late-developing countries through digestion and absorption. This paper aims to find out that if the e-cigarette, as a “first innovation” industry in a late-developing country, conform to the A-U model or conform to the “inverse A-U model”.

This paper takes the patent data of e-cigarettes from 2004 to 2021 as the research object, and uses Python’s Jieba segment words to divide product innovation and process innovation, and then uses statistical analysis methods to conduct empirical analyses on these data.

Thus, an improved A-U model suitable for the e-cigarette industry is proposed. In this model, product innovation in the e-cigarette industry appeared earlier than process innovation, but the synchronous development of product and process innovation is not lagging. The improved A-U model in the e-cigarette industry is not only different from the traditional A-U model but also does not conform to the inverse A-U model.

It is conducive to expanding and clarifying the theoretical contribution and applicable boundaries of the A-U model and has sparked thinking and exploration of the A-U model in e-cigarettes and emerging industries.

On this basis, suggestions on the development path and countermeasures of the e-cigarette industry are put forward.

Based on the e-cigarette industry, this paper takes patents as the research object and provides the method of dividing product innovation and process innovation, and proposes an A-U model suitable for the e-cigarette industry on this basis. By comparing the traditional A-U model with the inverse A-U model in latecomer countries, the background and causes of e-cigarette A-U model heterogeneity are analyzed from different stages and overall morphology. Based on this, the heterogeneity characteristics of e-cigarette innovation are summarized and sorted out.