Nowadays, environmental protection and sustainable development issues are being given considerable attention. To protect our environment, a series of policies have been legislated [1]. For example, a greenhouse gases emission reduction target have been set up by International organizations and national governments, it plans a 80% reduction for UK in 2050 [2]. In the meantime, a large number of enterprises are actively adopting advanced and innovative technologies to produce green or environmentally friendly products [3, 4, 5].

According to Ranjan and Jha [6], a green product has comparatively less effect on environment and less harmful on health than a traditional product. On the one hand, with the increase of customers’ environmental concerns, there are many convincing evidences that consumers’ attitudes toward green products have changed significantly [7]. A survey report with 9 developed countries shows that half of the respondents want to purchase green products, and 24% of the respondents are pleased to pay increased prices for buying green product [6]. On the other hand, in order to obtain a higher market share, enterprises would like to carry out appropriate marketing activities for green products in practise. Both of the two aspects mentioned above show that it is critically important to study green supply chain under marketing effort.

In addition, decision makers are usually assumed to be perfectly rational. However, many empirical and experimental studies have shown that decision makers exhibit bounded rationality in their decision process and have different social preferences [8, 9, 10, 11]. Fairness concerns is one of typical social preferences, which illustrates an enterprise’s concern regards to the inequality between supply chain members [12]. Usually, the fairness behavior of enterprises is caused by the uneven distribution of supply chain’ profits. When enterprises involve fairness behavior, they focus on their own income and fair treatment in profit allocation simultaneously [13]. For example, in March 2004, due to the demand for higher-than-normal kickbacks was rejected by Gree, a China’s household appliance retailer Gome decided to terminate its cooperation with Gree. This case reflects that Gome was concerned with distributional fairness and wanted to extract more profit from Gree by its dominating power in the retailing industry [14]. This reveals that we should pay more attention to the fairness behavior of enterprises when making decisions such as investment, pricing and designing contract.

Motivated by the above observations and discussions, in this paper, we study a green supply chain with a socially responsible manufacturer and a fair-mined retailer, where the manufacturer adopts advanced and innovative technologies to produce green products, and the retailer carries out marketing activities to obtain higher market share. We mainly focus on the optimal decisions about green quality level, marketing effort level, and pricing, as well as how to improve the supply chain’s economic and environmental performances. Meanwhile, we analyze the effect of the fairness behavior on the optimal decisions.

The main contribution of our study is threefold as follows. Firstly, we develop decentralized decision-making models with WP contract, and derive the optimal decisions for each member with a manufacturer Stackelberg game. Also, we use the centralized case to establish a performance benchmark. Secondly, we discuss the effect of the fairness behavior on the optimal strategies and profits. Thirdly, we propose a RCS contract to coordinate the supply chain and improve the supply chain’s performance.

The remainder of this paper is organized as follows. We review the relevant literature in next section. Section 3 presents the model setting, notations and assumptions. In Section 4, we use the centralized case to establish a performance benchmark. In Section 5, we develop decentralized supply chain models with WP contract under the scenarios whether the retailer involves fairness concerns or not. Several numerical investigations are given in Section 6. We conclude in Section 7.

This paper is closely related to the literature on green supply chain with marketing effort. Ranjan and Jha [6] investigated the pricing strategies and coordination mechanism in a dual-channel supply chain, where the market demand is a linear function consists of selling price, green quality level, and sales effort level. They proposed a surplus profit-sharing mechanism to achieve channel coordination. Basiri and Heydari [2] investigated the channel coordination issue in a two-stage green supply chain, in which the manufacturer produces green and traditional two substitutable products, and market demand for both products also be a function consists of retail price, green quality level and sales effort level. Li et al. [15] examined a low-carbon closed-loop supply chain (CLSC) under four different game structures and determined manufacturers’ carbon emission reduction level and retailers’ low-carbon promotion effort level. Gao et al. [16] considered a CLSC with price, collection effort and sales effort dependent demand and proposed coordination strategy for the decentralized supply chain. De Giovanni [17] investigated environmental collaboration via a reverse revenue sharing contract in a CLSC under the setting that the retailer invest in green advertising to build up the goodwill dynamic.

Some previous studies in conventional non-green environments which consider the product quality and marketing effort dependent demand are technically related to our paper. Nouri et al. [18] studied channel coordination of a manufacturer-retailer chain under a stochastic demand, in which the demand is dependent on the retailer’s promotional and the manufacturer’s innovation efforts. Huang et al. [19] addressed the coordination and profit allocation issues in a vendor-managed inventory supply chain via a combined contract composed of option and cost-sharing, where random demand is dependent on product quality level and marketing effort level. Ma et al. [20] investigated the issue of channel coordination for a two-stage supply chain under the demand is influenced by the retailer’s sales effort and manufacturer’s quality improvement efforts. Considering that both innovation and advertising contribute to the product demand, Song et al. [21] found that the optimal equilibriums under two different game structures, and proposed a new two-way subsidy policy to coordinate channel. Gurnani et al. [22] considered a two-echelon supply chain where the product supplier invests in quality improvement and the purchasing firm invests in the product market development via selling effort, and explored the impact of product pricing and timing of efforts investment. Liu et al. [23] also considered a supply chain with manufacturers’ product quality improvement effort and retailers’ sales effort improvement. They investigated the timing effect of retailer’s commitment of sales effort on the firms’ equilibrium investment and pricing decisions.

Another closely related literatures to our study is supply chain management (SCM) with fairness concerns. Cui et al. [12] was among the first to incorporate fairness concerns into SCM research using an analytical model, and investigated the role of WP contract in channel coordination under linear demand function. Then, the problem about SCM with fairness concerns is subsequently extended in different scenarios. Caliskan-Demirag et al. [24] extended Cui et al. [12] to allow nonlinear demand functions, and showed that compares with the linear demand function under the setting that the retailer is fair-minded, an exponential demand function is easier to achieve coordination. Zheng et al. [14] considered a three-echelon CLSC consisting of one manufacturer, one distributor, and one retailer, where the retailer exhibits fairness concerns. They investigated supply chain coordination by cooperative game approaches. Zhang et al. [25] examined the effects of consumer environmental awareness and retailer’s fairness concerns on the green product’s environmental quality, wholesale price and retail price in a manufacturer-retailer supply chain. Ma et al. [26] considered CLSC with retailer’s marketing-dependency demand under four reverse channel structures. They investigated how retailer’s fairness concerns affect optimal decisions and supply chain performance. Liu et al. [27] studied the effects of distributional fairness concerns and peer-induced fairness concerns on the order allocation’s decision-making in logistics service supply chain. Sharma [28] explored the impact of channel members’ fairness concerns on optimal decisions under the manufacturer-led Stackelberg game and vertical Nash game. Qian et al. [29] investigated a channel coordination problem in a two-echelon sustainable supply chain with a socially responsible manufacturer and a fair-minded retailer under cap-and-trade regulation.

As far as we know, no researches that address the optimal decisions and channel coordination problems in a green supply chain considering marketing effort and fairness concerns simultaneously. This paper deals with the gap in the literature. Most related works are found in Ma et al. [20] and Song et al. [21]. They investigated the optimal decisions and channel coordination issues of for a two-stage supply chain with one manufacturer and one retailer, where market demand is influenced by retail price and investment in product quality and marketing effort. But they assumed that both the manufacturer and the retailer are perfectly rational. Different from them, this paper considers a two-stage supply chain consisting of a socially responsible manufacturer and a fair-minded retailer, where market demand depends on green quality level, marketing effort level, and retail price. We focus mainly on the impact of the fairness behaviour on the optimal decisions and corresponding profits. Moreover, we examine how to coordinate the supply chain via a RCS contract combining revenue sharing and cost sharing, since revenue sharing contract is widely used to resolve channel conflict [30] and cost sharing contract is often used to coordinate the investments or efforts in both production and retail [19].

We consider a two-stage green supply chain consisting of one socially responsible manufacturer and one fair-minded retailer in a single period, in which the manufacturer produces green products and sells them to end consumers through the retailer. In order to satisfy the requirements of consumers, the manufacturer invests in green quality improvement, which lead the market demand increasing. In the meantime, in order to expand market and enhance demand, the retailer exerts marketing activities such as advertisement and promotional displays to publish the green information of products. In this case, the market demand of products depends on the retail price, green quality level and market effort level. Notations are listed in Table 1.

Notations.

Notation | Implication |
---|---|

production cost per unit of product | |

wholesale price per unit of product | |

retail price per unit of product | |

primary intrinsic demand | |

green quality level | |

marketing effort level | |

consumer’s sensitivity parameter in retail price | |

consumer’s sensitivity parameter in green quality level | |

consumer’s sensitivity parameter in marketing effort level | |

cost coefficient of greening investment | |

cost coefficient of marketing investment | |

fairness concerns coefficient of the retailer | |

revenue-sharing coefficient | |

cost-sharing coefficient | |

profit function | |

utility function |

Following the literature [16, 20, 31], the demand ^{2}/2 as the existing literature [32] did, in which ^{2}/2, where ^{2} > 0 and 2^{2} − ^{2} > 0.

Following the literature [20-21], we assume that the manufacturer acts as the leader in the supply chain, and first determine the green quality level and sets the wholesale price. Then, taking into consideration the green quality level and the wholesale price, the retailer decides its marketing effort level and the retail price. Customer demand takes place over the period and are satisfies without stockout during this time. The manufacturer is perfectly rational and aims to maximize its profit, while the retailer aims to maximize the utility since it involves fairness concerns.

In addition, subscripts

In this section, we investigate the centralized supply chain, the manufacturer and retailer joint operate as one decision-maker. Then the centralized supply chain’s profit is

Differentiating with respect to ^{I}^{I}^{I}

The Hessian matrix of
^{I}^{I}^{I}

The Hessian matrix is negative definite. This implies there exist unique optimal strategies (^{I*}^{I*}^{I*}

According to Proposition 1, we can obtain the channel maximum profit at ^{I*}^{I*}^{I*}

In the following sections, the decentralized system is investigated. We will discuss the effects of the retailer’s fairness concerns and propose a RCS contract model to coordinate the supply chain.

In the decentralized supply chain, a manufacturer-led Stackelberg game is considered. In this mode, the manufacturer acts as the leader and the retailer acts as the follower. We first explore the market effort level and retail price of retailer’s decision and then investigate the green quality level and wholesale price of the manufacturer’s strategy.

In this subsection, we assume that the retailer does not involve fairness concerns. Then in the WP contract model, the expected profits of the manufacturer and the retailer are

Given any fixed green quality level and wholesale price, the first order derivatives of
^{D}^{D}

The Hessian matrix of
^{D}^{D}

This implies that
^{D}^{D}

Substituting Eqs. (16) and (17) into Eq. (11) and differentiating with respect to ^{D}^{D}

The Hessian matrix of
^{D}^{D}

This implies that there exist unique optimal solutions (^{D*}, w^{D*}

Proposition 2 shows that the manufacturer’s profit can be maximized at ^{D*}^{D*}^{D*}^{D*}

Thus, the total channel profit of the supply chain in the decentralized system is

Moreover, conducting the comparison analysis, we can obtain that

In summary, we get the following Corollary.

^{D*} < g^{I*}, e^{D*} < e^{I*} and

Corollary 3 shows that all the optimal green quality level, market effort level and total profit of the supply chain in the decentralized supply chain with WP contract are less than that in the centralized system due to double marginalization. This implies that it is necessary to propose more effective contracts to mitigate the adverse impact of double marginalization, so as to improve the supply chain’s economic and environmental performances.

In this subsection, we discuss the scenario of a fair-minded retailer in the decentralized system with WP contract. Usually, we introduce the profit difference into the utility function to characterize the fairness concerns of decision-makers, and use the coefficient of fairness concerns to depict the impact of the fairness concerns caused by the profit difference between the manufacturer and the retailer. Following the literature [12], we assume that the equitable reference point of the retailer is the manufacturer’s profit. Thus, the retailer’s utility function with fairness concerns is

Thus, the utility function of the retailer, denoted as

Given any fixed green quality level and wholesale price, now we need to derive the retailer’s optimal market effort level and retail price by maximizing Eq. (36). Then, substituting the retailer’s optimal decisions into Eq. (13), we can solve the optimal green quality level and wholesale price of the manufacturer by profit maximizing. Thus, we get Proposition 3.

Proposition 4 shows that the manufacturer’s profit is maximized at

Further, we can get the optimal profits of the manufacturer and retailer, which can be characterized respectively as

Thus, the total channel profit of the supply chain in the decentralized system is

Let

Taking the first-order derivative of

Similarly, we have

In summary, we get Corollary 5.

Corollary 5 shows that with the fairness concerns coefficient increase, the optimal strategies, including green quality level, wholesale price, market effort level and retail price, decrease. All of the optimal solutions in fair-minded case are lower than that in the fair-neutral case. This reveals that the retailer’s fairness behavior will reduce not only its own investment in marketing effort but also the manufacturer’s investment in green quality. As a result, the impact of the retailer’s fairness behavior is expand and has a negative effect on the environmental performance of the supply chain.

Taking the first-order derivative of

Similarly, we have

In summary, we obtain the following corollary.

^{2}(2 + 3^{2}(1 +

Corollary 6 shows the impact of the retailer’s fairness behavior on the profits of the manufacturer, retailer and supply chain, as well as the impact of the retailer’s fairness behavior on its utility. It indicates that the manufacturer’s profit, supply chain’s profit and retailer’s utility are decreasing in the fairness concerns coefficient. Namely, the retailer’s fairness behavior always makes the manufacturer and total supply chain suffer in terms of profits. In addition, Corollary 6 reveals that the retailer’s optimal profit may be increasing or decreasing in the fairness concern coefficient. That is, the retailer can benefit from the fairness behavior as long as the retailer keeps the fairness concern at a proper level. However, the retailer’s utility is always decreased.

As we have proved, WP contract can not make the channel’s profit get the decentralized system. Then we introduce a RCS contract to improve the supply chain’s performance. Under the RCS contract, the retailer earns the revenue of per unit product in (1 −

Under the RCS contract, the expected profits of the manufacturer and the retailer are

When the retailer involves fairness concerns, given any fixed

Given any fixed green quality level

Proposition 7 shows that, under the RCS contract, the manufacturer’s profit is maximized at

Proposition 8 implies that the supply chain’s system-wide optimal performances are achieved under the RCS contract. Base on Proposition 7 and Proposition 8, the optimal profits of the manufacturer and retailer are

Obviously, we have

In this section, using several numerical investigations, we illustrate how the retailer’s fairness behavior affects the optimal decisions and profits, as well as how to share profit to achieve a win-win outcome under the RCS contract. We set the parameters as

We see from Figure 1 that all the optimal green quality level, wholesale price, market effort level and retail price are decreasing in the retailer’s fairness concerns coefficient. That is, the fairness behavior makes the retailer exert less marketing effort, and the manufacturer accordingly reduces the investment in green quality of products. This reveals that the fairness behavior has a negative effect on the supply chain performance, however, the consumer could benefit from the retailer’s fairness behavior due to the retailer would charge less when fairness concerns coefficient increase.

In the decentralized system with the WP contract, Figure 2 shows the effect of the fairness concerns coefficient on the optimal profits of the manufacturer, retailer and supply chain, as well as the effect of the fairness concerns coefficient on the retailer’ optimal utility. The optimal profit of the manufacturer is always decreasing in the fairness concerns coefficient, whereas the retailer’s optimal profit first increases and then decreases with the fairness concerns coefficient increase. In this numerical analysis, when 0 <

In the premise of supply chain coordination with the RCS contract, Figure 3 illustrates each party’s share on the channel profit of the supply chain. As we have proved previously, the manufacturer’s profit is decreasing in the wholesale price while the profit of the retailer is increasing in the wholesale price. We let

In this paper, a single period green supply chain consisting of a manufacturer and a retailer is studied. In this system, the manufacturer produces green products and sells them to end consumers through the retailer. Market demand depends not only on the retail price but also on the manufacturer’s green quality level and the retailer’s marketing effort level. The manufacturer is perfectly rational and aims to maximize its profit, while the retailer aims to maximize the utility since it involves fairness concerns. We mainly focus on the optimal decisions of each member and supply chain coordination problems.

First, we use the centralized case to establish a performance benchmark. Then, we develop decentralized supply chain models under the scenarios whether the retailer involves fairness concerns or not. We find that both the supply chain’s economic and environmental performances under WP contract are less than that under the centralized system. All the optimal green quality level, wholesale price, marketing effort level and retail price are decreasing in the retailer’s fairness concerns coefficient. Accordingly, the profits of both the manufacturer and the total supply chain are decreasing in the retailer’s fairness concerns coefficient. However, the retailer’s profit first increases and then decreases with the increase of the fairness concerns coefficient. Last, we introduce a RCS contract to coordinate supply chain. Under supply chain coordination, the manufacturer’s profit is decreasing in the wholesale price while the profit of the retailer is increasing in the wholesale price. It is proved that a win-win outcome is reachable by the RCS contract.

As a natural extension of our work, future research could be done by considering more complex supply chains with multiple manufacturers/retailers competing for more consumers with respect to green quality and marketing effort.

#### Notations.

Notation | Implication |
---|---|

production cost per unit of product | |

wholesale price per unit of product | |

retail price per unit of product | |

primary intrinsic demand | |

green quality level | |

marketing effort level | |

consumer’s sensitivity parameter in retail price | |

consumer’s sensitivity parameter in green quality level | |

consumer’s sensitivity parameter in marketing effort level | |

cost coefficient of greening investment | |

cost coefficient of marketing investment | |

fairness concerns coefficient of the retailer | |

revenue-sharing coefficient | |

cost-sharing coefficient | |

profit function | |

utility function |

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Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Application of improved RBF neural network algorithm in hierarchical management of enterprise Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network