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2024 Vol. 54, No. 8

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Mathematcis
Invariant measure for cubic Fibonacci-like polynomials
Wenxiu Ma
2024, 54(8): 0801. doi: 10.52396/JUSTC-2023-0036
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Abstract:
A special class of cubic polynomials possessing decay of geometry property is studied. This class of cubic bimodal maps has generalized Fibonacci combinatorics. For maps with bounded combinatorics, we show that they have an absolutely continuous invariant measure.
Mathematics
Yang–Mills bar connection and holomorphic structure
Teng Huang
2024, 54(8): 0802. doi: 10.52396/JUSTC-2023-0136
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Abstract:
In this note, we study the Yang–Mills bar connection $ A $, i.e., the curvature of $ A $ obeys $ \bar{\partial}_{A}^{\ast}F_{A}^{0,2} = 0 $, on a principal $ G $-bundle $ P $ over a compact complex manifold $ X $. According to the Koszul–Malgrange criterion, any holomorphic structure on $ P $ can be seen as a solution to this equation. Suppose that $ G = SU(2) $ or $ SO(3) $ and $ X $ is a complex surface with $ H^{1}(X,\mathbb{Z}_{2}) = 0 $. We then prove that the $ (0,2) $-part curvature of an irreducible Yang–Mills bar connection vanishes, i.e., $ (P,\bar{\partial}_{A}) $ is holomorphic.
Mean field analysis of interacting network model with jumps
Zeqian Li
2024, 54(8): 0803. doi: 10.52396/JUSTC-2023-0163
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Abstract:
This paper considers an $ n $-particle jump-diffusion system with mean filed interaction, where the coefficients are locally Lipschitz continuous. We address the convergence as $ n\to\infty $ of the empirical measure of the jump-diffusions to the solution of a deterministic McKean–Vlasov equation. The strong well-posedness of the associated McKean–Vlasov equation and a corresponding propagation of chaos result are proven. In particular, we also provide precise estimates of the convergence speed with respect to a Wasserstein-like metric.
Management
Trade credit contracting in a risk-averse supply chain under adverse selection and moral hazard
Zhihong Wang, Yuanyuan Xu, Yuwei Shao, Ziyi Chen, Yi Zhang
2024, 54(8): 0804. doi: 10.52396/JUSTC-2023-0077
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Abstract:
Trade credit, as an effective tool for integrating and coordinating material, information, and financial flows in supply chain management, is becoming increasingly widespread. We explore how a manufacturer can design optimal trade credit contracts when a risk-averse retailer hides its sales cost information (adverse selection) and selling effort level (moral hazard). We develop incentive models for a risk-averse supply chain when adverse selection and moral hazard coexist, which are then compared with the results under single information asymmetry (moral hazard). Moreover, we analyze the effects of private information and risk-aversion coefficient on contract parameters, selling effort level and the profit or utility of the supply chain. The study shows that when the degree of retailer’s risk aversion is within a certain range, reasonable trade credit contracts designed by the manufacturer can effectively induce the retailer to report its real sales cost and encourage it to exert appropriate effort. Furthermore, we find that the optimal trade credit period, optimal transfer payment, and retailer’s optimal sales effort level under dual information asymmetry are less than under single information asymmetry. Numerical analysis are conducted to demonstrate the effects of the parameters on decisions and profits.
A hybrid trade-old-for-new and trade-old-for-remanufactured supply chain with carbon tax
Yu Dong, Wuqing Liao
2024, 54(8): 0805. doi: 10.52396/JUSTC-2022-0148
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Abstract:
Facing serious environmental problems, governments and manufacturers are taking action to reduce carbon emissions. Among these endeavors, carbon tax policy are widely adopted by governments, trade-old-for-new (TON) and trade-old-for- remanufactured (TOR) are offered by manufacturers and subsidized by governments. To explore the effects of remanufacturer competition and carbon tax on the manufacturer’s TON and TOR decisions and the environment, we formulate three profit maximization models and present some theoretical and numerical analyses. The results show that, under the remanufacturer competition and carbon tax, the manufacturer’s optimal price and production decisions mainly depend on consumer willingness and carbon tax rate. A higher consumer willingness to manufacturer’s remanufactured products will decrease the demand for the manufacturer’s TON, but it always increases the demand foe the manufacturer’s TOR. A higher consumer willingness to remanufacturer’s products will not affect the demand for the manufacturer’s TON; however, it will reduce the demand for manufacturer’s TOR. In addition, we find that a higher carbon tax rate always reduces total carbon emission reduction, and it may increase the manufacturer’s profit due to the increase in TOR demand.
Supply chain coordination with inventory risk allocation
Qingyi Wu, Shuang Xie
2024, 54(8): 0806. doi: 10.52396/JUSTC-2023-0134
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Abstract:
Unlike the traditional decentralized channel, the drop-shipping channel entails a retailer relaying consumers' orders to the manufacturer, which proceeds to stock the orders and directly ship them to the consumers. This study explores supply chain coordination and product quality in drop-shipping and traditional channels. Specifically, we analyze the performance of both channels under wholesale price and revenue-sharing contracts. Our study yields several key findings. First, the revenue-sharing contract can coordinate both traditional and drop-shipping channels, effectively increasing supply chain performance. Second, given the channel structure, the retailer prefers the wholesale price contract, whereas the manufacturer prefers the revenue-sharing contract. Third, product quality is higher in the drop-shipping channel when demand uncertainty is high. Finally, the implementation of the revenue-sharing contract increases product quality in the traditional channel, whereas it keeps product quality unchanged in the drop-shipping channel.

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