In recent years, with the rapid development of Internet information technology, we have entered the era of big data. More and more Internet users begin to enjoy the convenient experience brought by online shopping and mobile payment, and they choose to purchase the services or goods they need online [1]. Under such a market background, how to win over high-quality and stable customer base is an important factor to ensure the robust growth of enterprises, at the same time, stable and repeatable customers are the source power for the continuous development of e-commerce enterprises [2, 3]. According to the survey results of China Internet Network Information Development Center [4], nearly 10% of the users in the whole e-commerce market will automatically terminate their contact with one e-commerce platform and switch to another in half a year, which makes the customer mobility of the e-commerce platform appear to be greater. In addition, most customers have less repeat purchase behaviour, which makes the customer churn rate of the e-commerce platform relatively high. In this non-contractual environment, customer relationship is not constrained, which makes it difficult to predict and define the loss.

In recent years, the research on prediction of customer churn through data mining technology has gradually increased [5, 6]. Analysing a series of browsing behaviour data such as search, click, collection and evaluation of users on the e-commerce platform can help enterprises to understand the purchase process, preference and habits of users, as well as the content of interest, etc., and combining with the dimensional subdivision of data can provide more targeted services to customers and provide support for enterprise personalised service strategy, so as to meet the needs of different levels of customers, and improve their satisfaction [7,8]. However, the abovementioned researches mainly focus on the algorithm accuracy or model fusion optimisation, while the research on more comprehensive customer feature description is less. Meanwhile, the definition of customer churn in the model is dualistic, and the description of process dynamics is slightly insufficient [9, 10]. Therefore, by fully considering the characteristics of the e-commerce industry, and combining with the current situation of customer churn of e-commerce enterprises, we can deeply understand the substantive problems behind the customer churn, so as to build an early warning model of customer churn on e-commerce platform. It can effectively predict and judge the possible risk of customer churn for enterprises in the future.

Customer churn in e-commerce enterprises refers to the phenomenon that users temporarily or permanently terminate the transaction relationship with e-commerce enterprises and no longer accept the products or services provided by e-commerce enterprises [11]. As a kind of general customer churn, it is a kind of customer churn under the non-contractual relationship situation.

The loss of customers can be defined as shown in Figure 1.

When individuals feel or think that the quality or benefits of an organisation are declining, there are three choices: exit, voice and loyalty. Therefore, customer churn is defined as the user's behaviour to terminate the relationship with the enterprise/organisation, which can be summarised as: cancellation, transfer, suspension, etc. If the customer gives up the cooperation with the original enterprise and turns to other enterprises for some reasons, it is generally considered as the loss of the customer.

In the judgement based on the transaction behaviour of customers, customer churn is the process in which the existing customers terminate the activities of enterprise products and services and purchase corresponding products and services from other enterprises or competitors. All the indicators that can describe the customer's trading behaviour are used for the judgement basis. For example, customers in a certain period of time, there will be a larger trading cycle.

In the actual transaction process, there is a kind of customers whose purchase frequency or frequency of products and services provided by the enterprise is only slightly lower than before, but not completely turn to zero. Therefore, customer churn should be classified into two categories: one is based on change of process and the other is based on change of final state [12].

By comparing the above three types, it can be seen that the definition based on the customer result status is a method that directly divides the loss status according to certain business relationship rules, which is easier to identify and more obvious to distinguish customers. But it will make the partition result too one-sided, once the rules are limited, thus the whole prediction judgement will become inflexible; The other method is based on the judgement of the change of customer's trading behaviour, and observes the change in the process of user's transaction behaviour from multiple dimensions, and can trace the cause of the loss based on the final state result.

This paper adopts the definition method based on transaction behaviour; once the value of the observation dimension exceeds or is lower than the preset threshold, then the customer status is determined as churn.

In order to more accurately define and describe customers, understand the behaviour characteristics and preferences of customers, and then provide targeted marketing for them. Managers often choose to construct user portrait features and behaviour characteristics, which can maintain long-term interactive relationship with customers according to their own understanding of customers.

As shown in Figure 2, Recurrence, Frequency, Monetary (RFM) model can better measure customer value. The model includes three indicators [13, 14]: R (recency), F (frequency) and M (monetary) reflecting the customer's latest consumption interval. They represent respectively that during the observation period, the time interval between the last consumption behaviour of users and the observation point, the total number of consumption behaviours of users in the observation period, and the total consumption of customers in the observation period.

It reflects the time interval between the customer's last consumption behaviour and the observation point in the observation period. The larger value of indicator R means that customers have not purchased anything on the platform for a long time, and they are in the decline period of life cycle and who are about to be lost, and the customer value of such customers will be lower. On the contrary, the smaller the R value is, the closer the time interval between the customer's last shopping and the observation point, the higher the customer value.

Indicator F is a measure of the number of times customers spend in the inspection period. Generally speaking, the higher the frequency of customers’ consumption, the higher the value. While the shorter the last consumption interval and the higher the consumption frequency in the observation period, the higher the comprehensive value of such customers and the more economic benefits they can bring to enterprises, which should be the focus of the enterprise.

This is the most important measurement index of customer value. The higher the consumption amount, the higher the contribution, and the higher the customer value. By synthesising these three indicators, the value of customers to the enterprise can be described in a multi-dimensional way, and according to the different combination performances of different customer groups with the three indicators, some of their behaviour characteristics can be analysed.

Customer's life cycle describes the transformation process of customer's state from establishing contact to ending contact between customer and enterprise, and reflects customer's characteristic performance in each stage of enterprise. In order to explore the key to customer churn, many researchers are committed to the study of customer change characteristics in various stages of the life cycle [15, 16]. As shown in Figure 3, the whole life cycle is divided into five stages as follows:

In this period, enterprises explore potential customers from the market by means of marketing, and customers also understand the actual situation of enterprises through various kinds of information, so as to preliminarily understand each other and lay the foundation for the development of follow-up relations.

In this period, with each product or service linkage between the two sides, the satisfaction and cooperation intention between the two sides will accelerate development, and the interdependence relationship will also deepen.

Due to the interaction in the first two stages, enterprises and customers will have more and more understanding in this period, so the relationship between them is further improved where all kinds of contact and cooperation relations are gradually become stable and for enterprises, this is the golden period with customers.

Due to poor communication, or competition from other companies, the established good customer relationship before has deteriorated gradually and the customers showed various negative performances, and the transactions gradually slowed down. However, it should be realised that the deterioration of the relationship may occur at any stage of the whole customer cycle, which is not limited to the last stage of the life cycle.

After the recession stage, customers lose their trust on the enterprise at last, which make them to end the business contact with the enterprise. At this stage, the customers are completely lost.

With the theoretical study of the life cycle, we can intuitively understand the stage of customer churn, and help enterprises to develop better customer retention strategies after the subsequent analysis of customer churn.

The early warning of customer churn management occurs before the real loss of customers, which can be sensitive to the impact of customer churn dynamic factors; once there is movement, it will send a signal to remind enterprises to take necessary measures to improve the status quo. The early warning management of customer churn can not only help enterprises to achieve their goals, but also prevent them from falling into severe difficulties, which is important to improve enterprise's own value and realise excellent management. As shown in Figure 4, it usually includes the following aspects [17, 18]:

Detecting the signs of customer churn needs to be carried out under a comprehensive plan. It is the first step for enterprises to predict customer churn in order to reduce the number of customers churn. The main job of detecting the signs of customer churn is to detect the customers who are about to be lost in real time.

Judgement of customer churn, that is, after detecting the signs of customer churn, scientific methods are used to get the index data for in-depth analysis of the index data which exposed customer behaviour characteristics, thus helps to judge the tendency of customer churn.

Evaluation of customer churn should be carried out after the completion of the previous links. After the data of customer churn sign detection link is saved, these index data are analysed in depth, and the abnormal indicators are scored and summarised, and then graded according to different severity. Finally, the enterprise formulates a reasonable weight determination standard according to the actual situation; comprehensive evaluation of the customer churn status of enterprises is made by comprehensive factors.

The concept of customer churn warning determines that the system can be used to monitor customers with significant churn tendency. However, in order to effectively solve the problem of customer churn, it is necessary to construct a comprehensive, scientific and reasonable customer churn early warning model on the premise of deeply exploring the early warning mechanism and mode of customer churn.

Cluster analysis is a multivariate statistical method, which refers to grouping abstract objects into sets of similar elements. It is usually used to study the classification of samples or indicators [19]. The essence of clustering analysis is to reasonably and fully replace unknown information with known information, classify and identify the essential attributes of grey system, and obtain objective quantitative analysis results.

The sample data is clustered by K-means, and 100 samples are clustered into four types of churn risk states, namely: safe (A), less safe (B), dangerous (C) and very dangerous (D). The cluster analysis and evaluation description of each risk state are shown in Table 1.

Classification of customer churn risk levels.

Safety (A) | 14% | Most of these users think that the platform has fast response speed, beautiful interface, convenient use, good customer service, payment method that can meet the basic needs of users, fast delivery speed, satisfaction with the service of delivery staff. |

Less safe (B) | 35% | However, such users sometimes give up payment because they can’t find a suitable way, and worry about whether their payment security and personal privacy will be leaked from time to time. They have a high degree of participation in product evaluation, high requirements for products and will return and exchange products whose descriptions don’t match the real ones for a long time. |

Danger (C) | 20% | These users usually feel that the response speed of the platform is slow, their satisfaction with the products recommended by the e-commerce platform is low and their delivery speed and delivery staff service are often not satisfied. There is no dependence on the exclusive sales of products, and they think that the prices of most products are somewhat high, and the participation in the evaluation of purchased products is also low. |

Very dangerous (D) | 31% | Their satisfaction with the platform is very low, which is usually reflected in the dissatisfaction with the aesthetics and convenience of the interface, the quality of the goods and the service of the delivery staff. |

The e-commerce transaction is divided into several links, such as registration and login, interface browsing, payment, commodity purchase and after-sales service. Therefore, on the basis of previous research literature, considering the obvious characteristics of e-commerce enterprises and combining the actual situation of e-commerce enterprises in China, the index system shown in Figure 5 is constructed.

In this paper, the early warning model based on neural network is adopted, and the three-layer network topology is selected according to the data of training sample and prediction sample, as well as indicators of early warning mentioned earlier. The network structure is shown in Figure 6.

It is located at the bottom of the neural network, where neurons in this layer receive pre-selected indicators as input information from the external environment. In the neural network model of this paper, the number of neurons in the input layer is determined by the input amount of index data and 15 normalised index data of early warning of customer churn are respectively input as input samples, which are used to predict the crisis situation of customer churn.

(2) The hidden layer, in which the hidden layer nodes find out the hidden rules from the sample data, and then store the information in the form of connection weights. In summary, the following four formulas can be used to calculate hidden nodes:

Among them

In this paper, the four empirical formulas are used to calculate the number of nodes in the four hidden layers, and the different nodes are put into the neural network for training. Then, the sample data of test set is brought into the neural network for fitting and the prediction accuracy of the output layer data obtained is compared with the expected result of the test set sample. The number of hidden layer nodes with the highest prediction accuracy 8 is selected as the number of hidden layer nodes in the early warning model.

It is located at the highest level of the network. At this level, the neural network transmits the hidden layer data to the output neuron, which in turn transmits the information to the external environment. The data category of the output layer determines the number of neurons in the output layer.

In this paper, when the network output layer is defined, the alert levels are determined in four levels according to different levels of customer churn risk. The result of the first-level warning level corresponding to the output layer is [0001], the second-level warning level corresponding to the output layer is [1000], the third-level warning level corresponding to the output layer is [0100] and the fourth-level warning level corresponding to the output layer is [0010].

The customer churn warning system of e-commerce platform based on neural network mainly processes data through transfer function and training function, and tests the training effect of the model by learning rate and expected error.

Transfer function is usually selected from purelin, tansig and logsig. As there are negative values in the input data, in order to prevent data compression from affecting the accuracy, the tansig function that can map the neuron input range from (−∞, +∞) to (−1,1) is selected as the transfer function of hidden layer, and its expression is:

In addition, as the expected output data of the output layer are [1000], [0100], [0010] and [0001], this paper determines that the transfer function from the hidden layer to the output layer is the logsig function, which maps the input range of neurons from (−∞, +∞) to (0, 1), and its function is

Trainlm is selected as the training function in this paper. When the number of network weights is small, it can quickly converge, and has strong advantages in improving training speed, which avoids falling into local minimum. It is suitable for the function fitting of small and medium-sized networks, with fast convergence and small error.

In order to ensure the stability of the network, we usually try to choose a small learning rate while ensuring the training duration. The most scientific and reasonable method is to first determine the learning rate of several different values, and then, after the training of neural network, select the most appropriate learning rate according to the descending speed of the error function. Generally, the range of selection is between 0.01 and 0.8. Through the test, the learning rate of 0.01 is chosen.

Usually, the smaller the expected error value is, the more accurate the model. However, if the expected error value is too small, the number of hidden layer nodes will be increased unintentionally, resulting in the extension of the training time of neural network. Meanwhile, it will greatly increase the risk of ‘over-fitting’ of the network in training, which directly leads to the reduction of the universality of the neural network. In this paper, the following indicators are used for calculation:

Mean absolute error

Sum square error

Mean square error
_{j}_{j}_{j}

Generally, the expected error is between 0.0001 and 0.01. The expected error is set to 0.001 with the help the test.

After the neural network model with good fitting degree is obtained, it is necessary to test the early warning accuracy of the established, so as to verify whether the prediction accuracy of the model meets the requirements. First, the early warning index data of customer churn risk of sample users collected in the above survey is used as input layer data and input into the neural network, and after the processing of the hidden layer network, the output layer data is obtained. By comparing the output results obtained by hidden layer processing with the actual output results, the smaller the error value, the higher the fitting degree of the early warning model based on neural network to the variables of output. In general, the high fitting degree represents the high applicability and generalisation ability of the early warning model.

By further transforming the output results of neural network, the risk warning grades of ten test set samples from the model constructed can be obtained. After transformation, we can get the output results of test set samples, and the comparison between the customer churn risk warning grades and the expected output is shown in Table 2.

Test results of early warning model.

(0, 0, 0, 1) | (0, 0, 0, 1) | Correct | A |

(0, 0, 0, 1) | (0, 0, 0, 1) | Correct | A |

(0, 1, 0, 0) | (0, 1, 0, 0) | Correct | C |

(0, 0, 1, 0) | (0, 0, 1, 0) | Correct | D |

(0, 0, 1, 0) | (0, 0, 1, 0) | Correct | D |

(0, 1, 0, 0) | (0, 1, 0, 0) | Correct | C |

(0, 0, 1, 0) | (0, 0, 1, 0) | Correct | D |

(0, 1, 0, 0) | (0, 1, 0, 0) | Correct | C |

By comparing the expected output of the test set sample with the output of the early warning model based on neural network, it can be seen that the forecast of the risk warning is in the sequence of first-level warning, first-level warning, third-level warning, fourth-level warning, fourth-level warning, third-level warning, fourth-level warning and third-level warning. The result of actual output is completely consistent with the expected output and so the accuracy rate has reached 100%, which means that the prediction data obtained by this early warning model is not far from the real data, and the prediction accuracy rate of it is high.

Based on the phenomenon of customer churn in e-commerce enterprises, this study puts forward the early warning of risk for enterprises. By summarising the related research results of customer churn theory and risk early warning of enterprise, this paper extracts 15 risk early warning indicators about customer churn of e-commerce, constructs the risk early warning model of e-commerce customer churn by using neural network, and tests this model. The results show that the early warning index system of customer churn risk in China's e-commerce enterprises designed in this paper is scientific and reasonable. The early warning system of customer churn risk of e-commerce platform based on neural network has excellent generality, and its prediction accuracy is 100%, which can provide important reference value for the early warning research of customer churn risk in the whole e-commerce industry.

#### Classification of customer churn risk levels.

Safety (A) | 14% | Most of these users think that the platform has fast response speed, beautiful interface, convenient use, good customer service, payment method that can meet the basic needs of users, fast delivery speed, satisfaction with the service of delivery staff. |

Less safe (B) | 35% | However, such users sometimes give up payment because they can’t find a suitable way, and worry about whether their payment security and personal privacy will be leaked from time to time. They have a high degree of participation in product evaluation, high requirements for products and will return and exchange products whose descriptions don’t match the real ones for a long time. |

Danger (C) | 20% | These users usually feel that the response speed of the platform is slow, their satisfaction with the products recommended by the e-commerce platform is low and their delivery speed and delivery staff service are often not satisfied. There is no dependence on the exclusive sales of products, and they think that the prices of most products are somewhat high, and the participation in the evaluation of purchased products is also low. |

Very dangerous (D) | 31% | Their satisfaction with the platform is very low, which is usually reflected in the dissatisfaction with the aesthetics and convenience of the interface, the quality of the goods and the service of the delivery staff. |

#### Test results of early warning model.

(0, 0, 0, 1) | (0, 0, 0, 1) | Correct | A |

(0, 0, 0, 1) | (0, 0, 0, 1) | Correct | A |

(0, 1, 0, 0) | (0, 1, 0, 0) | Correct | C |

(0, 0, 1, 0) | (0, 0, 1, 0) | Correct | D |

(0, 0, 1, 0) | (0, 0, 1, 0) | Correct | D |

(0, 1, 0, 0) | (0, 1, 0, 0) | Correct | C |

(0, 0, 1, 0) | (0, 0, 1, 0) | Correct | D |

(0, 1, 0, 0) | (0, 1, 0, 0) | Correct | C |

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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 -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