Let us define A = Circ r (a 0 , a 1 , . . . , a n-1 ) to be a n × n r-circulant matrix. The entries in the first row of A = Circ r (a 0 , a 1 , . . . , a n-1 ) arewhere F i and L i are the ith Fibonacci and Lucas numbers, respectively. This paper gives an upper bound estimation of the spectral norm for r-circulant matrices with Fibonacci and Lucas numbers. The result is more accurate than the corresponding results of S Solak and S Shen, and of J Cen, and the numerical examples have provided further proof.

Currently, environmental, social, and corporate governance (ESG) has become an all-pervasive term in the industrial sector, owing to its significant impact on corporate decision-making. While most of the studies provide evidence that the ESG significantly improves a firm's performance and value in the long run, few studies quantitatively analyzed the linkage between ESG and total factor productivity (TFP). Using the data of Chinese-listed companies during 2010–2020, we found that there is a positive relationship between ESG performance and TFP. ESG also improves the corporate TFP by reducing the financial constraints and improving the innovation input. Our extended analysis revealed that this beneficial effect tends to be stronger for SOEs (state-owned enterprises) and industries with high pollution levels. This study also brought to light some implications for Chinese firms in relation to their ESG practices and sustainable development.

We use a new method of matrix decomposition for r -circulant matrix to get the determinants of A n = Circ r F 1 , F 2 , … , F n and B n = Circ r L 1 , L 2 , … , L n , where F n is the Fibonacci numbers and L n is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.

In the operation and management of the company, major customers may affect a supplier firm’s level of governance. The goal of our study is investigating whether a major customer acts as an important role in corporate governance in emerging markets and exposing the mechanism that how major customers affect corporate decision-making. There is a growing body of literature involving studies about the effect of customer concentration on firm performance of western countries. Few studies have recognized to what degree does customer concentration satisfy the sustainable development of supplier firm. Using a sample of Chinese listed firms, we found a nonlinear relationship between customer concentration and risk-taking, corporate policies and firm performance. Evidence shows that the effect of customer concentration in China resembles an inverted U-shaped curve and major customers are crucial in financial and investment policies. Our results help to provide a broader perspective on the role of major customers, giving a deep explanation about the role of customer concentration in corporate governance.

Supply chain information disclosure is a vital factor for corporate investment efficiency and can signal a corporation’s long-term sustainable development. However, little attention has been paid to its significance. In this paper, we investigate how supply chain information disclosure affects corporate investment decisions. Using a sample of Chinese-listed firms, we find that firms that disclose nonfinancial information are more likely to have a high level of investment efficiency. We also identify the mechanism underlying the effect by examining the mediating effect of financial constraints and agency costs. Increasing a firm’s supply chain information disclosure can improve its investment efficiency by reducing its financial constraints and agency costs. We further find that this positive impact is more pronounced for non-state-owned enterprises (non-SOEs) and firms located in regions with a high degree of marketization. Our findings imply that supply chain information disclosure plays an important role in corporate investment efficiency and sustainable development. Our study emphasizes the importance of nonfinancial information disclosure, contributing to the literature investigating the role of supply chain management in corporate decision-making on sustainable development.