Against the continuous impact of the international financial crisis, the economy is in a stage of continuous differentiation, which presents a slow recovery and development trend, the trade pattern in the world is constantly being adjusted and changed, the global supply chain tends to be flat and China’s traditional foreign trade business has been facing a downturn in recent years. Especially, the competitiveness of small- and medium-sized enterprises (SMEs) is obviously weakened, the cost of enterprise resources and other factors keeps rising and there is a strong demand for a new way of foreign trade. Under such a condition, cross-border e-commerce (CBEC) came into being [1–3]. The main body of the CBEC market is made up of SMEs, which will help them to internationalise [4]. CBEC is characterised by low cost and low trade barriers so that it broadens the channels for SMEs to enter the overseas markets, and at the same time give them the opportunity to participate in the global economy [5, 6].

The business model of the CBEC is “Internet + Made in China + cross-border trade”, which is an innovation of the traditional foreign trade model and is characterised by competition, inclusiveness, freedom and openness. The development of Internet technology provides technical support for the development of CBEC, and online shopping has become an important consumption platform all over the world. Goods purchased through CBEC are not only cheap, but also rich in categories, and the ways of obtaining them are more convenient and diversified [7, 8].

CBEC is the inevitable trend in trade development. CBEC, which has the advantages of high efficiency, low cost and taking the Internet to realise transactions in foreign trade, is increasingly becoming the development bottleneck brought about by the traditional foreign trade mode, thus making companies to enter new market or global value chains. However, for traditional foreign trade, SMEs, for example, will be restricted by technology, capital, manpower, material resources and other conditions in their operation, and the cost of a self-built CBEC platform is high. Therefore, it is appropriate to use third-party CBEC platforms to transform the CBEC industry at the initial stage, which will be with relatively low risk and a high success rate [9–11]. The CBEC platform is one of the important channels for consumers to communicate with enterprises, and it is also a vital way for enterprises to directly connect with commodity inspection agencies, customs agencies and cross-border logistics [12]. For SMEs, the choice of relevant platforms is crucial, which will determine whether the CBEC industry of SMEs can develop smoothly in the future. Therefore, in the rational allocation of the CBEC platform, using data analysis to evaluate it objectively and accurately can provide a scientific decision for enterprises.

To construct a comprehensive evaluation index system of the CBEC platform, it is necessary to combine the actual situation of enterprises with the characteristics of the platform, and establish scientific, comprehensive, objective and rigorous principles on the evaluation index. The details are as follows:

The comprehensive evaluation index system should comprehensively analyse the comprehensive functional characteristics of platforms, such as logistics services, third-party payment services, customer groups and popularity.

Taking scientific principles as scientific evaluation indicators, the characteristics of the CBEC platform are highlighted by objective results. Based on the theory, combined with the practical application of enterprises, the scientific, reasonable, reliable and practical evaluation indexes at all levels are ensured.

The comparability here is also called unity, which emphasises horizontal comparison and refers to the comparability between different CBEC platforms. At the same time, the calculation measures of the evaluation index selection must be unified, and each index can not only reflect the characteristics of each platform but also facilitate for collection and operation.

In order to reflect the characteristics of the platform scientifically and rigorously, the comprehensive evaluation index system can not only consider qualitative factors, but also deal with them quantitatively, so as to facilitate calculation and analysis, and make the index reflect the characteristics of the platform more scientifically and reasonably.

CBEC is global, real-time, paperless and low-cost, which is different from the traditional foreign trade and domestic e-commerce, so the evaluation index should be typical. The setting of a comprehensive evaluation index system should fully consider the quality of service and system of the CBEC platform.

It is necessary to consider the dynamic changes in the CBEC platform characteristics in different periods to ensure the long-term rationality of the evaluation indicators.

Based on the above principles and a large number of literature summaries, the dimensions of system function, cost, service quality and platform quality are finally determined as the first-level indicators, including 16 second-level indicators, as shown in Figure 1. The construction of a comprehensive evaluation index system, it will lay the foundation for the choice of CBEC for SMEs.

B11 security and reliability: the security and reliability of the platform system means that the platform can protect and keep confidential the user’s account and private information, which provide a safer network environment for users and enhance their sense of security and trust.

B12 Data analysis function: The platform has the function of data analysis, and it does not need any third-party tools to provide the seller with the required operation and management data, assist them in analysing the target market and related business analysis, and at the same time provide the seller’s real transaction data to the buyer.

B13 ERP support: the platform cooperates with third-party managers to share information and data, thus simplifying the seller’s internal operation and management. Through the ERP system, not only can the complicated supply chain process inside the seller be simplified, but also the defect of data transmission that the platform system function cannot complete can be made up.

B21 Logistics service: Consumers’ shopping experience will be affected by timeliness, logistics attitude and price. Parcel, overseas warehouse, dedicated-line logistics and international express delivery are all important components of CBEC logistics.

B22 Third-party payment service: the platform of the third-party payment is involved in CBEC transactions as service providers, and they can quickly process the transaction information of buyers and sellers by simplifying the tedious transmission between banks. This method of payment is safe and efficient, and is widely favoured by users.

B23 Overseas warehouse service: Platform overseas warehouse mainly refers to the CBEC platform and enterprises delivering goods to sales destinations individually or cooperatively, and managing goods, warehousing, picking, packaging and delivery in this process.

B24 Foreign exchange settlement service: it can realise the exchange and sharing of data and information among enterprises, customs and related administrative departments. The platform can provide declaration of agent customs, foreign exchange settlement and tax refund for merchants.

B31 Visits in platform: platform visits include Alex ranking, which refers to the frequency of visitors and traffic on the platform. The more the visits and traffic, the more helpful it is for the order conversion rate of the merchant store.

B32 Matching degree: Different platforms have different positions and ideas. The seller needs to judge the groups of customer and distribution of the platform, and choose the platform that matches his target market. Whether the functions, characteristics, attributes and uses of the products are within the category of hot-selling products in the platform should be considered.

B33 Marketing method: this mainly refers to the orientation of customer group and pricing method, etc.

B34 Operation and management mode: this mainly refers to the rigid requirements of the platform in operation and management, that is, whether inventory backlog is required.

B41 Entry fee: platform entry fee, also known as member service fee, means that the platform provides a trading place for the seller, and the seller must be charged a certain percentage of management fee. After paying the member service fee, the seller can enjoy various services provided by the platform.

B42 Value-added service fee: After the buyers and sellers become members of the platform, the platform will charge the buyers and sellers a certain percentage of value-added service fee, which covers booth promotion, pay-per-click and bidding ranking, etc.

B43 Commission of transaction: merchants register for free, and only charge a certain commission according to different industries and different proportions after the successful transaction between buyers and sellers.

B44 Transaction fee: merchants register with the platform free of charge. After the successful transaction between the buyer and the seller, the platform will charge the seller a certain percentage of transaction fee for payment to the transaction provider.

B45 Marketing fee: Marketing and promotion fee is the operation and management fee charged by the platform to assist enterprises in product promotion.

AHP is a multi-criteria decision-making form combining quantitative and qualitative analysis. It is characterised in that on the basis of analysing the essence, the decision-making process of complex problems is presented mathematically with less quantitative information. Through data to solve complex decision-making problems with multi-objectives, multi-criteria or no structural characteristics, the purpose of simplifying the decision-making scheme is achieved [13, 14].

As shown in Figure 2, the general steps of AHP mainly include four steps. The first step is to build the hierarchical structure model; second, construct the judgement matrix; third, obtain hierarchical single sorting and its consistency check; and finally implement hierarchical general ranking and its consistency check.

The decision to solve the problem is divided into three levels, namely, the target level, the decision criterion level and the decision scheme level. In the application of AHP, the problem to be solved is to calculate the relative weight of the bottom layer to the top layer, so as to sort the schemes and measures at the bottom layer and choose the best scheme [15, 16]. In this way, the objective of independent direction, variables to be thought of (choice models) and choice items are partitioned into the most significant level, the centre level and the least level as per their relationship.

The construction of a judgement matrix is to determine the weight of the target layer by comparing each element with each other pairwise. In the AHP, the importance of each element in the judgement matrix is quantitatively displayed by introducing a scale of 1–9. A size of 1 demonstrates that two components are of equivalent significance, and a size of 9 shows that the previous is a higher priority than the last option. The proportional of scale demonstrates the significance of looking at the trade request of two elements.

The comparative judgement matrix of

Hierarchical single sort refers to the evaluation of all elements in pairs for an element in the previous layer, and arrange the important order. The concrete calculation can be carried out according to the judgement matrix A, and the calculation can ensure that it can meet the characteristic root and characteristic vector conditions of AW = λ_{max} W, where the largest feature root of A is λ_{max}, and the normalised feature vector corresponding to λ_{max} is W, _{i}_{ij}

The calculation steps of the weight vector (W) and the maximum feature (λ_{max}) are as follows:

First of all, take the product of the row elements according to Eq. (2), and then raise it to the

Then, it is normalised into a ranking weight vector by formula (3), which is denoted as W, then _{i}_{1},_{2}, ⋯ ,_{n}^{2}
is the result of judging the hierarchical single ranking of the matrix.

Finally, determine the maximum characteristic root of the matrix by Formula (4):

If the _{max} can be obtained by the following methods:

The following consistency index (CI) is taken to test the CI of judgement:

CI = 0 means that the judgement matrix is completely consistent, and the larger the CI, the more serious the inconsistency of the judgement matrix.

Assuming that _{1}, _{2}, …, _{m}

Set the B layer as _{1}, _{2} …, _{n}_{j}_{j}_{j}

When

The maximum eigenvalue _{max}

Weight calculation of primary index

System function | Platform quality | Quality of service | Cost | Weight value | |
---|---|---|---|---|---|

System function | 1 | 3 | 4 | 7 | 0.369381 |

Platform quality | 1/4 | 1/4 | 1 | 4 | 0.461749 |

Service quality | 1/3 | 1/3 | 4 | 4 | 0.122011 |

Cost | 1/7 | 1/7 | 1/4 | 1 | 0.069144 |

Where

CT, consistency index; CR, consistency ratio.

Similarly, the weights of secondary indicators below the primary indicators can be calculated in turn, and the weights of secondary indicators are shown in Tables 2–5 in turn.

Weight calculation of system function

B11 Safety and reliability | B12 Data analysis function | B13 Support ERP | Weight value | |
---|---|---|---|---|

B11 Safety and reliability | 1 | 4 | 7 | 0.587033 |

B12 Data analysis function | 1/4 | 1 | 4 | 0.287321 |

B13 Support ERP | 1/7 | 1/4 | 1 | 0.125646 |

The maximum characteristic value _{max}

CR, consistency ratio.

Weight calculation of service quality

B21 logistics service | B22 third-party payment service | B23 overseas warehouse service | B24 foreign exchange settlement service | Weight value | |
---|---|---|---|---|---|

B21 logistics service | 1 | 1/3 | 1/4 | 1/2 | 0.072149 |

B22 third-party payment service | 3 | 1 | 1 | 4 | 0.218498 |

B23 overseas warehouse service | 4 | 3 | 1 | 7 | 0.642498 |

B24 foreign exchange settlement service | 2 | 1/7 | 1/4 | 1 | 0.069144 |

The maximum characteristic value = 4.230717 and the CR = 0.086411 <0.1 (rounded). Through the consistency test, the weight value can be used.

CR, consistency ratio.

Weight calculation of platform quality

B31 platform visits | B32 matching degree | B33 Marketing Mode | B34 operation management mode | Weight value | |
---|---|---|---|---|---|

B31 Visits | 1 | 1 | 2 | 1 | 0.252149 |

B32 Matching degree | 1 | 1 | 1 | 2 | 0.338498 |

B33 Marketing Mode | 1/4 | 3 | 1 | 2 | 0.162498 |

B34 Operation management mode | 1 | 1/2 | 1/4 | 1 | 0.053144 |

The maximum characteristic value _{max}

CR, consistency ratio.

Weight calculation of cost

B41 platform entry fee | B42 Value-added service fee | B43 transaction commission | B44 transaction fee | B45 Marketing and promotion fee | Weight value | |
---|---|---|---|---|---|---|

B41 Entry fee | 1 | 1 | 5 | 7 | 3 | 0.399572 |

B42 Value-added service fee | 1 | 1 | 4 | 2 | 3 | 0.294969 |

B43 Transaction commission | 1/4 | 3 | 1 | 1 | 3 | 0.116201 |

B44 Transaction fee | 1/3 | 1/2 | 1 | 1 | 2 | 0.111480 |

B45 Marketing and promotion fee | 1/4 | 1/4 | 1/4 | 1/2 | 1 | 0.077777 |

The maximum characteristic value _{max}

Take Amazon, a CBEC platform, as an example, to evaluate the fuzzy comprehensive index. 20 executives from the foreign trade department of X Company were investigated and interviewed, and the comment sets involved were arranged into five categories according to the order of priority, including “most consistent, very consistent, consistent, generally consistent and non-consistent”. Fuzzy evaluation method is used to process the questionnaire data, and finally the best option is selected.

Evaluation set: v = {1,2,0} = {most consistent, very consistent, consistent, generally consistent and non-consistent}, and the corresponding numerical sets are 90,75,60,45,30, respectively.

Weight set: the index weight set is established according to the above-mentioned secondary index weight.

According to the survey results, the subordinate subsets of the Amazon platform in system function evaluation are as follows:

Therefore, its fuzzy evaluation matrix is:

After normalisation, the evaluation value of “system function” membership degree is as follows:

Similarly, the membership of service quality, platform quality and cost are as follows:

According to the above evaluation system, except for Amazon, the membership degrees of the four platforms of AliExpress, Wish and Lazada are evaluated, and the final evaluation scores of the four platforms are calculated. The results are shown in Table 6: most consistent, very consistent, consistent, generally consistent and non-consistent

Evaluation scores of different CBEC platforms

Most consistent | Very consistent | Consistent | Generally consistent | Non-consistent | Score | Rank | |
---|---|---|---|---|---|---|---|

Amazon | 0.238 | 0.420 | 0.249 | 0.083 | 0.0013 | 80.20 | 1 |

Lazada | 0.020 | 0.521 | 0.359 | 0.09 | 0 | 74.36 | 2 |

AliExpress | 0.086 | 0.248 | 0.523 | 0.124 | 0.019 | 62.68 | 4 |

Wish | 0.078 | 0.314 | 0.441 | 0.139 | 0.020 | 66.85 | 3 |

CBEC, cross-border e-commerce.

According to the above scores, the Amazon platform has the highest evaluation score, which is consistent with the questionnaire results of X company executives. Digital e-commerce platform evaluation can provide suggestions for companies to match the CBEC platforms.

When making decisions, managers of cross-border enterprises must not only consider many intangible qualitative factors, but also make the best choices according to the judgement of quantitative factors. Therefore, in this paper, an evaluation index system of the CBEC platform was constructed by AHP and fuzzy evaluation method to quantify enterprise management. The results show that in this paper, the total ranking of the 16 evaluation indicators selected by this paper all passed the consistency test, and four e-commerce platforms, including Amazon, were evaluated by fuzzy analysis. Among them, the Amazon platform scored the highest, with 80.20 points, which was consistent with the comprehensive evaluation of enterprise executives, thus providing suggestions for companies to match CBEC platforms.

#### Weight calculation of primary index

System function | Platform quality | Quality of service | Cost | Weight value | |
---|---|---|---|---|---|

System function | 1 | 3 | 4 | 7 | 0.369381 |

Platform quality | 1/4 | 1/4 | 1 | 4 | 0.461749 |

Service quality | 1/3 | 1/3 | 4 | 4 | 0.122011 |

Cost | 1/7 | 1/7 | 1/4 | 1 | 0.069144 |

#### Weight calculation of service quality

B21 logistics service | B22 third-party payment service | B23 overseas warehouse service | B24 foreign exchange settlement service | Weight value | |
---|---|---|---|---|---|

B21 logistics service | 1 | 1/3 | 1/4 | 1/2 | 0.072149 |

B22 third-party payment service | 3 | 1 | 1 | 4 | 0.218498 |

B23 overseas warehouse service | 4 | 3 | 1 | 7 | 0.642498 |

B24 foreign exchange settlement service | 2 | 1/7 | 1/4 | 1 | 0.069144 |

#### Weight calculation of cost

B41 platform entry fee | B42 Value-added service fee | B43 transaction commission | B44 transaction fee | B45 Marketing and promotion fee | Weight value | |
---|---|---|---|---|---|---|

B41 Entry fee | 1 | 1 | 5 | 7 | 3 | 0.399572 |

B42 Value-added service fee | 1 | 1 | 4 | 2 | 3 | 0.294969 |

B43 Transaction commission | 1/4 | 3 | 1 | 1 | 3 | 0.116201 |

B44 Transaction fee | 1/3 | 1/2 | 1 | 1 | 2 | 0.111480 |

B45 Marketing and promotion fee | 1/4 | 1/4 | 1/4 | 1/2 | 1 | 0.077777 |

#### Weight calculation of system function

B11 Safety and reliability | B12 Data analysis function | B13 Support ERP | Weight value | |
---|---|---|---|---|

B11 Safety and reliability | 1 | 4 | 7 | 0.587033 |

B12 Data analysis function | 1/4 | 1 | 4 | 0.287321 |

B13 Support ERP | 1/7 | 1/4 | 1 | 0.125646 |

#### Weight calculation of platform quality

B31 platform visits | B32 matching degree | B33 Marketing Mode | B34 operation management mode | Weight value | |
---|---|---|---|---|---|

B31 Visits | 1 | 1 | 2 | 1 | 0.252149 |

B32 Matching degree | 1 | 1 | 1 | 2 | 0.338498 |

B33 Marketing Mode | 1/4 | 3 | 1 | 2 | 0.162498 |

B34 Operation management mode | 1 | 1/2 | 1/4 | 1 | 0.053144 |

#### Evaluation scores of different CBEC platforms

Most consistent | Very consistent | Consistent | Generally consistent | Non-consistent | Score | Rank | |
---|---|---|---|---|---|---|---|

Amazon | 0.238 | 0.420 | 0.249 | 0.083 | 0.0013 | 80.20 | 1 |

Lazada | 0.020 | 0.521 | 0.359 | 0.09 | 0 | 74.36 | 2 |

AliExpress | 0.086 | 0.248 | 0.523 | 0.124 | 0.019 | 62.68 | 4 |

Wish | 0.078 | 0.314 | 0.441 | 0.139 | 0.020 | 66.85 | 3 |

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Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses 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 Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road 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 Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE 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 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 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 -groupsResearch 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 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