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Lu Liu
College of Economics and Management, Shandong University of Science and Technology, Qingdao, Shandong 266590, China

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Journal article
Published: 29 April 2020 in Advances in Mathematical Physics
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Let G be a simple and undirected graph. The eigenvalues of the adjacency matrix of G are called the eigenvalues of G. In this paper, we characterize all the n-vertex graphs with some eigenvalue of multiplicity n−2 and n−3, respectively. Moreover, as an application of the main result, we present a family of nonregular graphs with four distinct eigenvalues.

ACS Style

Linming Qi; Lianying Miao; Weiliang Zhao; Lu Liu. Characterization of Graphs with an Eigenvalue of Large Multiplicity. Advances in Mathematical Physics 2020, 2020, 1 -5.

AMA Style

Linming Qi, Lianying Miao, Weiliang Zhao, Lu Liu. Characterization of Graphs with an Eigenvalue of Large Multiplicity. Advances in Mathematical Physics. 2020; 2020 ():1-5.

Chicago/Turabian Style

Linming Qi; Lianying Miao; Weiliang Zhao; Lu Liu. 2020. "Characterization of Graphs with an Eigenvalue of Large Multiplicity." Advances in Mathematical Physics 2020, no. : 1-5.

Journal article
Published: 24 March 2020 in Mathematical Problems in Engineering
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Many small and medium enterprises (SMEs) with capital constraints often have no access or find it costly to obtain a loan from a bank; the retailer tends to borrow money from other enterprises in the supply chain by trade credit financing. We consider an emission-dependent supply chain with one emission-dependent manufacturer and one capital-constrained retailer in need of financing to explore the optimal operational and environmental strategies of a low-carbon supply chain under trade credit financing. We use a Stackelberg game model to depict the low-carbon supply chain. We analyse the optimal carbon-emission reduction effort, wholesale price, and order quantity in the equilibrium state. The impacts of key parameters, such as the retailer’s internal working capital, the manufacturer’s risk-aversion degree, and the carbon-trading price on the supply chain operation, are analysed. The results show that the retailer’s capital constraint causes the carbon-emission reduction effort, wholesale price, and order quantity to improve synchronously. The supply chain achieves a win-win outcome for both the manufacturer and the retailer when the capital-constrained retailer is funded via trade credit from the manufacturer. The in-depth development of financing is beneficial to the manufacturer but is a disadvantage for the retailer. When the initial carbon-emission quota is low, the manufacturer benefits from a relatively lower carbon-trading price. Otherwise, a higher carbon-trading price is better for the manufacturer. The “carbon-trading price trap” ensures that the retailer’s profit is minimal. We further investigate the scenario in which the manufacturer is risk averse and find that the retailer will purchase fewer products and that the manufacturer will gain less profit to decrease the carbon-emission reduction effort. The manufacturer’s risk aversion is unfavourable to both the economic and environmental outcomes of the whole supply chain. This research provides strategic support for a low-carbon supply chain to carry out operational decisions in the context of enterprise capital constraint. To examine the theoretical results, the data used in the existing literature are further used to simulate the corresponding conclusions. Our research enriches the existing supply chain finance literature and provides decision support for the supply chain core enterprise.

ACS Style

Linming Qi; Lu Liu; Liwen Jiang; Zicheng Wang; Weiliang Zhao. Optimal Operation Strategies under a Carbon Cap-and-Trade Mechanism: A Capital-Constrained Supply Chain Incorporating Risk Aversion. Mathematical Problems in Engineering 2020, 2020, 1 -17.

AMA Style

Linming Qi, Lu Liu, Liwen Jiang, Zicheng Wang, Weiliang Zhao. Optimal Operation Strategies under a Carbon Cap-and-Trade Mechanism: A Capital-Constrained Supply Chain Incorporating Risk Aversion. Mathematical Problems in Engineering. 2020; 2020 ():1-17.

Chicago/Turabian Style

Linming Qi; Lu Liu; Liwen Jiang; Zicheng Wang; Weiliang Zhao. 2020. "Optimal Operation Strategies under a Carbon Cap-and-Trade Mechanism: A Capital-Constrained Supply Chain Incorporating Risk Aversion." Mathematical Problems in Engineering 2020, no. : 1-17.

Journal article
Published: 19 March 2019 in Sustainability
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The need for low-carbon development has become a social consensus. Increasing numbers of enterprises implement carbon emission reduction by using carbon cap-and-trade mechanisms to cater to consumers and practice social responsibility. From the manufacturer’s perspective, they can implement carbon emission reduction investment by themselves or outsource it to the retailer or energy service company (referred as ESCO). To explore the best carbon emission reduction mode selection strategy, we built and compared three carbon emission reduction modes—manufacturer emission reduction, retailer emission reduction, and ESCO emission reduction—by using Stackelberg game models. The joint decisions of operation, finance, and environment were obtained by using the backward induction approach. The impacts of key parameters were analyzed, such as the retailer’s initial capital amount and the decision-makers’ risk aversion degree on the low carbon supply chain operation. Our results show that the optimal carbon emission reduction mode for the manufacturer is changed as the retailer’s initial capital amount changes. Carbon emission reduction by the ESCO (retailer) becomes the dominant strategy for both the economy and environment when the cost advantage (cash investment ratio) of the ESCO (retailer) carbon emission reduction mode is sufficiently high (low). Overall, decision-makers’ risk aversion is detrimental to both the economic and environmental developments of the supply chain. We also designed contracts to realize the coordination of risk-neutral, risk-averse, capital-adequate, and capital-constrained low-carbon supply chains. These results give guidance for decision-makers to better manage the low-carbon supply chain in the context of fully considering the influential factors of risk aversion and capital constraint.

ACS Style

Weisheng Deng; Lu Liu. Comparison of Carbon Emission Reduction Modes: Impacts of Capital Constraint and Risk Aversion. Sustainability 2019, 11, 1661 .

AMA Style

Weisheng Deng, Lu Liu. Comparison of Carbon Emission Reduction Modes: Impacts of Capital Constraint and Risk Aversion. Sustainability. 2019; 11 (6):1661.

Chicago/Turabian Style

Weisheng Deng; Lu Liu. 2019. "Comparison of Carbon Emission Reduction Modes: Impacts of Capital Constraint and Risk Aversion." Sustainability 11, no. 6: 1661.