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Considering the phenomenon of the mean reversion and the different speeds of stock prices in the bull market and in the bear market, we propose four dynamic models each of which is represented by a parameterized ordinary differential equation in this study. Based on existing studies, the models are in the form of either the logistic growth or the law of Newton's cooling. We solve the models by dynamic integration and apply them to the daily closing prices of the Taiwan stock index, Taiwan Stock Exchange Capitalization Weighted Stock Index. The empirical study shows that some of the models fit the prices well and the forecasting ability of the best model is acceptable even though the martingale forecasts the prices slightly better. To increase the forecasting ability and to broaden the scope of applications of the dynamic models, we will model the coefficients of the dynamic models in the future. Applying the models to the market without the price limit is also our future work.

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PurposeEducational reform is a complex undertaking and the interactions between leaders as they go about a change are consequential for realizing desired outcomes. Advice relationships are one such interaction and can play a key role in driving knowledge transfer and development and as such are an important social capital asset supporting organizational change. Building on the growing scholarship around a social network approach to understanding educational leadership and systems change, the study draws from network concepts to examine advice relationships within a district-wide leadership team as the leaders engages a reform initiative, and what accounts for the development of these important relational ties.Design/methodology/approachQuantitative data were collected through an annual survey at six points over six years from the leadership team in one public school district in the Western United States, including perceptions of organizational learning, beliefs about reform, and reform-related advice relationships.FindingsUsing multilevel mixed modeling, findings reveal downward trends in leaders' advice-seeking and -receiving ties over time and that seeking and receiving advice is positively related to organizational learning, beliefs about reform impact, or beliefs about their efficacy in implementing the reform. However, views about reform-related resources are negatively associated with seeking and receiving advice ties over time.Originality/valueThis study contributes to the literature on the social side of change specifically related to leadership, reform, organizational learning, and leader beliefs about reform implementation. Further, the work offers practical implications for potential social infrastructure design for joint work.