This article constructs a nonlinear differential equation model that incorporates non-defective return factors and minimizes the expected cost of the inventory control problem under the cross-border e-commerce overseas warehouse model. Under the dynamic background, the problem of pricing and shop assistant decision-making in the supply chain is studied, and the differential game model is constructed. We use differential game theory to give pricing and store assistance strategies under decentralized and centralized decision-making. At the same time, we designed a contract to achieve supply chain coordination in this context. Numerical examples calculate the optimal return price and optimal order quantity under supply chain coordination.

#### Keywords

- Nonlinear differential equation
- Cross-border e-commerce
- Return rate

#### MSC 2010

- 34A34

As market competition continues to intensify, allowing customers to return goods has become a means of competition widely adopted by retailers. For example, JD.com and Tmall allow customers to return unsatisfied products. Returning goods will incur logistics, inspection, and repackaging costs [1]. It is estimated that the US electronics industry spent 13.8 billion US dollars in processing returns in 2007. The main reason for returns is that the products cannot match the needs of customers. Therefore, how to reduce the product return rate is an important issue that retailers face to solve. Current methods to reduce product returns include improving the product design quality, charging replacement fees, and shortening product delivery time. In addition, providing store assistance services can also effectively reduce the product return rate.

Research on customer returns is relatively rich. Some scholars have studied the supply chain decision-making problems affected by returns under different channel structures and gave the chain members' preference for channel structure selection. Some scholars assume that the amount of refunds affects demand and solves the problem of inventory decision-making and return policy formulation in the supply chain. These documents focus on analyzing the impact of customer returns without considering the issue of reduction in return rates. Some scholars believe that store ancillary services can reduce the unreasonable return rate of products and improve the impact of the return rate on market demand. He gave the product pricing and dual-channel strategy of competing companies. Some scholars have further studied the issue of how companies choose to store auxiliary service strategies. The results show that the strength of the difference in the return rate affects the company's strategic choices [2]. Some scholars have constructed a shop assistant decision-making model in the context of asymmetric customer return information. Some scholars have extended the store-assisted decision-making problem to the VMI scenario.

In recent years, certain results have been achieved in studying supply chain optimization and coordination issues affected by returns from a dynamic perspective [3]. By establishing a differential game model and solving the problem, the supply chain's optimal pricing and store-assisted strategy under the background of consignment sales are given. Design a dynamic consignment price contract to achieve supply chain coordination. However, the study did not fully consider the return processing costs caused by product returns and the impact of returns on demand, which is not completely consistent with the actual situation.

This article comprehensively considers the impact of product return rate on market demand. Research on the pricing of supply chain and auxiliary decision-making of stores in a dynamic context. The article uses differential game theory to give pricing and store assistance strategies under decentralized and centralized decision-making. At the same time, a contract is designed to realize supply chain coordination under this background.

This article considers a supply chain consisting of a manufacturer and a retailer. The manufacturer produces the product and sells the product to the end consumer through the retailer. Retailers allow consumers to return unsatisfactory products after purchasing products [4]. The returned products can be sold again but will incur disposal costs for the retailer. In addition, retailers can reduce the return rate of products by improving store assistance to increase product sales and profits.

_{M}_{R}_{i}

In the context of the research of this article, the level of store assistance is related to the store assistance efforts invested by retailers. The following differential equation describes it:

_{0} represents the initial store assistance level.

The product return rate

_{max} ∈ (0, 1) is a constant, which represents the maximum return rate possible for this type of product.

Store assistance cost is the quadratic function of store assistance effort, that is, ^{2}(

Under centralized decision-making, all members of the supply chain decide the price of the product and the auxiliary strategy of the store, namely decision

The optimal path for the store assistance level is

In

And
_{C}

To solve the optimal control problem, we introduce the common state variable _{C}

Because of the application of the principle of maximum value, the optimal decision should meet the following conditions:

From equation (10) and equation (11), we can get

We substitute equations (13) and (14) into (1) and (12),

In

Two characteristic roots of matrix B

In

The eigenvector corresponding to the eigenroot of matrix B

Then the solution of the system of differential equations can be expressed as

Determine the constants _{1} and _{2} according to the conditions _{0} and
_{1} < 0 needs to be assumed here, namely

So you can get

Then we get _{C}

Note that

The optimal strategy under centralized decision-making has a formula

This shows that the higher the efficiency of store assistance level in reducing the product return rate, the more store assistance efforts are invested [6]. The level of store assistance will be correspondingly higher, but the price will be lower. Shop assistance efforts to improve the level of shop assistance efficiency will also produce similar results.

The form of the wholesale price in this contract is ^{E}_{M}^{E}_{M}

Then the retailer accepts the contract and maximizes its profits to determine the product's retail price and the store's extra service efforts.

The fee-based contract can achieve supply chain coordination. The objective function of the retailer under this contract is

Introduce the common state variable

We can get the optimal decision under the contract

The optimal decision under the contract is the same as that under the centralized decision so that the supply chain can be coordinated by a two-part fee contract [8]. The optimal profit of the retailer and the manufacturer under the contract is

To ensure that the two members accept the contract, the parameters in the contract need to meet the condition
_{1} < _{2} two members of the supply chain are willing to participate in implementing the two-part fee contract. Among them
_{1}, _{2}) are the feasible regions of the two-part fee contract.

It is assumed that the influence of store assistance level on product return rate and product retail price and return rate on market demand is linear. This linear characterization can reflect the relationship between these quantities and is widely used in existing studies [9]. Of course, it is more accurate to describe the nonlinear structure, but it is more difficult to solve the model and excavate the meaning of management.

This section mainly discusses the impact of system parameter changes on the stable values of product pricing, store assistance efforts and store assistance level, and coordination contracts through numerical examples. Assume parameter _{0} = 3, _{max} = 0.3,

Figure 1 and Figure 2 show that the optimal store assistance level and store assistance effort under centralized decision-making are higher than the corresponding values under decentralized decision-making. This shows that centralized decision-making is more conducive to improving the level of store assistance [11]. In addition, whether it is centralized or decentralized decision-making, the level of store assistance and store assistance efforts increases with store assistance efficiency or store assistance effort efficiency. On the contrary, the retail price of the product becomes smaller. From Figure 3 and Figure 4, it can be seen that when falls between, and the supply chain can be coordinated, and the income of each member is better than in the case of decentralized decision-making. In addition, as the parameters continue to increase, the win-win area will continue to grow larger.

This paper uses differential game theory to study supply chain pricing and store auxiliary strategy issues and designs contracts in a dynamic environment to coordinate the supply chain. Studies have shown that centralized decision-making is conducive to promoting the supply chain to improve store assistance efforts. Still, centralized decision-making does not always mean that the supply chain should lower retail prices. The two-part fee contract designed in this paper can realize supply chain coordination.

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Research on sustainable design of sports centre based on algorithm verification Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Informatisation of educational reform based on fractional differential equations Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Nonlinear Differential Equations in Preventing Financial Risks Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Application of regression function model based on panel data in bank resource allocation financial risk management Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Image denoising model based on improved fractional calculus mathematical equation The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Evaluation and Verification of Patent Value Based on Combination Forecasting Model Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations The Law of Large Numbers in Children's Education Data structure simulation for the reform of the teaching process of university computer courses Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Good congruences on weakly U-abundant semigroups Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Fed-UserPro: A user profile construction method based on federated learning Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching 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 Computer Vision Communication Technology in Mathematical Modeling 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 in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations 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 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 Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm 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 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 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 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 Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method 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 Video adaptive watermark embedding and detection algorithm based on phase function equation Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model