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How different types of financial service providers support small- and mediumenterprises under the impact of COVID-19 pandemic: From the perspective of expectancy theory

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Frontiers of Business Research in China 2020年第4期14卷 448-474页

作者： Hua Song Yudong Yang Zheng Tao Business School Renmin University of ChinaBeijing 100872China

The 2019 novel coronavirus disease(COVID-19)pandemic has significantly impacted several aspects of the society and the economy.A problem that needs prompt attention in this situation is the increasing difficulties faced by small-and mediumsized enterprises(SMEs)in raising capital,which has aroused great concern from multiple stakeholders such as public administrations and regulators.As the major supply of capital,financial service providers(FSPs)play a critical role in financing SMEs.However,how FSPs deal with SME financing during shocks has not yet been fully researched.Accordingly,in this study,a theoretical framework based on expectancy theory is proposed to explore the expected strategic adjustments of FSPs in financing SMEs.Specifically,this study investigates 272 FSPs in China on their expectancy and attitude on financing to SMEs during the COVID-19 pandemic.Furthermore,this study has divided FSPs into three categories:commercial banks,non-bank financial institutions,and credit-enhanced FSPs.Differences among these categories are compared and analyzed.

关键词： 2019 novel coronavirus disease(COVID-19)pandemic Financial service providers(FSPs) expectancy theory Financing to small-and medium-sized enterprises(SMEs)

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The Analysis of Convergence for the 3<i>X</i>+ 1 Problem and Crandall Conjecture for the a<i>X</i>+ 1 Problem

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Advances in Pure Mathematics 2021年第5期11卷 400-407页

作者： Zuojun Hu Huadian Jinsha River Upstream Hydropower Development Co. Ltd. Chengdu China

The 3X + 1 problem (Collatz conjecture) has been proposed for many years, however no major breakthrough has been made so far. As we know, the Crandall conjecture is a well-known generalization of the 3X + 1 problem. It is worth noting that, both conjectures are infamous for their simplicity in stating but intractability in solving. In this paper, I aim to provide a clear explanation about the reason why these two problems are difficult to handle and have very different characteristics on convergence of the series via creatively applying the probability theory and global expectancy value E(n) of energy contraction index. The corresponding convergence analysis explicitly shows that a = 3 leads to a difficult problem, while a > 3 leads to a divergent series. To the best of my knowledge, this is the first work to point out the difference between these cases. The corresponding results not only propose a new angle to analyze the 3X + 1 problem, but also shed some light on the future research.

关键词： 3X + 1 Problem Crandall Conjecture Energy Method expectancy theory

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