The economy in the e-commerce environment, based on informatisation and digitalisation, brings sellers and buyers into a brand-new information world without distance. Customers can obtain product-related information through various channels, ranging from passive consumption to fully rational analysis of product-related information, and then choose products or services that are really suitable for them. It can be said that customers in the e-commerce environment are becoming more and more mature [1]. On the other hand, with the transformation of the global economy, many industries are experiencing the problem of oversupply, forcing enterprises to reform their foothold from products to customers, which makes most businesses to involve in the fierce competition for customers [2]. In the e-commerce environment, the relationship between enterprises and customers has completely changed. In the fierce competition within the industry, the core management of the enterprise has gradually transformed from ‘product-centred’ to ‘customer-centred’, that is, only by meeting the customers’ need in a fastest and best way, can they continuously attract new customers and sustain old customers [3]. The first thing in the customer-centred approach is to classify customers reasonably. In the face of a large number of customer information and data, which are limited to superficial records and lack of in-depth analysis, it is indispensable to select a method for effective classification of customers [4].

The significance of this research is mainly reflected in three aspects: Firstly, applying the BP neural network to the actual classification of e-commerce customers can not only expand the application field of the BP neural network itself but also better analyse complicated factors in practical problems, which reflects the value of the BP neural network in the commercial field [5]. Secondly, the information of marketing activities is counted to predict the purchase tendency of consumers, so as to achieve accurate prediction of e-commerce customers, which results in the accurate prediction on the premise of extracting reasonable indicators of classification information. Finally, the improved customer classification model is used to distinguish customers with different purchasing tendencies for e-commerce, so that e-commerce companies can provide targeted, differentiated and effective marketing services for different customers, which not only reduces the cost but also improves the marketing profit and brings convenience to the management of relationship with e-commerce customers. Based on this, in this work, the main BP neural network algorithm is used to study the classification of e-commerce customers.

The customers’ demands are infinite, and the limited resources owned by enterprises cannot meet the needs of all customers. In order to maximise social benefits as much as possible, enterprises must make rational use of limited resources and strive for high-value customers, which requires enterprises to have the ability to judge the value of customers. By implementing market segmentation by means of technology, enterprises can identify customers who can promote the development and then focus the limited resources on these potential customers [6]. According to the existing research, it is found that the measurement indexes of customer classification are diverse and the process is complicated, which mainly includes the following points: Firstly, enterprises should build an index system of customer classification. Different products and services of enterprises determine the difference in selected indicators. Therefore, enterprises should choose appropriate indicators according to the characteristics of their target customers [7]. At present, customer consumption involves a lot of information, including not only the basic attribute information of customers, such as customer gender, age and education level, but also other information of customer consumption, such as consumption frequency, total consumption amount and consumption satisfaction [8]. Secondly, enterprises should use big data to sort out the collected data, or other information technology methods to process the data; understand the customer consumption characteristics in a certain way; and calculate the customer value quantitatively [9]. Thirdly, according to the calculated customer value, enterprises should classify and manage customers and put forward appropriate suggestions for each type of customers to obtain maximum benefits [10]. The process of customer classification is shown in Figure 1.

Compared with the characteristics of customer classification in the traditional business environment, customer classification in the e-commerce environment has changed a lot:

Classification indicators: Classification indicators are diversified. In the environment of e-commerce, enterprises classify customers not only by relying on customer value or some basic characteristics of customers but also by adding some log files left by customers on the Internet, from which personalised factors such as customers’ use feelings, psychological changes, preferences and habits can be analysed. These indicators can more realistically reflect the real needs of customers [11].

Customer-centred approach: In the environment of e-commerce, customers are becoming more and more mature and elusive and have transformed from passive consumption to active consumption, which is the main driver of transaction. Therefore, in order to attract new customers and retain old customers, enterprises must consider customers as the centre and classify customers. The classification results obtained in this way can help them design a complete set of network marketing schemes according to different types of customers [12].

Complete customer information: In the environment of e-commerce, the means for enterprises to obtain customer information has suddenly expanded with the application of the Internet. Enterprises can obtain detailed information and data of customers through various channels, which can truly reflect the real needs of customers [13].

Combining qualitative and quantitative analyses: In the e-commerce environment, in order to meet the increasing personalised, diversified and mature needs of customers, enterprises generally adopt the customer classification method combining qualitative and quantitative analyses to classify customers. This not only integrates the advantages of the two methods but also overcomes the shortcomings of the two methods, which make the classification result more reasonable [14].

Real-time information: In the e-commerce environment, due to the use of the Internet, the barriers of time and space have been broken. Enterprises and customers can use one-to-one, one-to-many and many-to-many online communications in real time, including text, voice and video, which results in more targeted information [15].

Choosing appropriate indicators is the key to the quality of customer classification results. A good classification indicator system should follow the following principles.

The scientific principle: The selection of indicators must have a theoretical basis, and indicators without practical significance cannot be selected. Generally speaking, the selection of indicators should follow the combination of science and practice, dynamic and static, and qualitative and quantitative [16].

The principle of comprehensiveness and independence: When selecting indicators, enterprises should try their best to consider them comprehensively from different aspects so as to keep the independence and representativeness of the indicators.

The principle of appropriateness: One of the principles that a qualified classification index must possess is appropriateness. When selecting customer classification indicators, it is necessary to have a clear distinction and reflect the specific information of customers. The appropriateness of the index must be judged in advance, and the corresponding verification should also be carried out for the customer classification. The principle of appropriateness not only reflects in the selection of indicators but also requires appropriateness in the employment of indicators.

The principle of measurability: A qualified classification index must be measurable to help study and compare the behaviours and attitudes of each customer group towards the specified products. When selecting indicators, it is better to avoid the indicator system, which is not easy to analyse or measure [17].

The principle of operability: The measurement and data collection of the customer classification index values should be feasible.

The principle of availability: The results of customer classification should be practical.

Generally, selecting the customer classification index in the e-commerce environment is an extremely critical and complicated process. In order to ensure the effective development of classification, it is necessary to combine the particularity and interactivity of enterprises to construct a classification indicator suitable for the actual situation of enterprises [18–22].

This work will build a customer classification index system from the following three dimensions: characteristics of e-commerce customers, current values and potential values of the customers. The index system established from the aforementioned dimensions can also calculate the value of e-commerce customers more comprehensively and scientifically, as shown in Figure 2.

Characteristics of e-commerce customer

According to the existing research and practical basis, it can be found that the characteristics of e-commerce customers mainly include six secondary indicators: age, income, education level, geographical location, trust and customer interaction value. At the age of 26–40 years, the scale of monthly active users of Internet is the largest, and according to statistical data, it is also found that the middle-aged group is the main service target of e-commerce [23]. From the perspective of education level, the proportion of Internet users with junior high school education is the largest, followed by senior high school/technical secondary school education. As e-commerce is a new thing, the higher the education level, the greater the acceptance, so it can be considered that the customer value of those with a high education level is greater. From the perspective of income, Internet users with a monthly personal income of 3,001–5,000 yuan account for the largest proportion in China. Secondly, for the network users with 5,001–8,000 yuan and above 8,000 yuan, the consumption of e-commerce products especially needs the support of income, so it can be considered that the customer value above 8,000 yuan is relatively the largest [24]. Enhancing customers’ trust in the e-commerce platform and regional advantages and bringing good shopping experience to customers are conducive to enhance customers’ aspiration to consume. Therefore, it can be considered that customers with better geographical location have greater value.

Current value of customer

According to the existing research on the current value of customers, most scholars measure the benefits that customers bring to enterprises by applying the recency, frequency and monetary of them. Therefore, through the modification of RFM, the index for calculating the current value of customers is obtained. There are three specific indexes: firstly, the last time a customer spent on the e-commerce platform from now on, – generally, the shorter the time, the more enthusiastic the customer is about e-commerce consumption and the greater the customer value; secondly, the number of times that customers purchased on the e-commerce platform in the last year – the more times, the higher the dependence of customers on cross-border consumption and the greater the customer value; third, the total amount the customers spent on the e-commerce platform in the last year and the higher the amount the customers are willing to spend on the e-commerce platform – the more customers trust cross-border consumption, the greater the customer value [25].

Potential value of customers

The factors involved in the potential value of customers are quite complicated, including the structural changes of customers’ demands for products, which shows that customers not only repeatedly need purchased products but also may be interested in other products of enterprises. This also include customers’ psychological satisfaction with products and loyalty to enterprises, which mainly show that customers prefer this kind of products, customers love the product design, and culture publicity is effective [26]. Generally speaking, the more the customers’ demands for enterprise products and the more satisfied and loyal they are to enterprise products, the greater the customer value [27]. The customer potential value built in this study includes seven secondary indicators, namely, the number of repeated purchases for customers, the number of cross-purchases by customers, the durability of the relationship between customers and enterprises, the degree of customers’ perception of enterprise brand image, whether they are willing to recommend others to buy, customers’ scores and customers’ willingness to become members.

The e-commerce customer classification index system is constructed from the customer characteristics, current value and potential value, which comprehensively considers all factors that may affect the customer value, and it is scientific to calculate the customer value with this index system. According to the existing literature research, realistic statistical data and cases, an e-commerce customer classification index system is established, which is shown in Table 1.

Classification index system about e-commerce customer based on customer value.

Customer age | |

Customer income level | |

Customer characteristics of e-commerce | Customer education |

Geographical position | |

Degree of trust | |

Customer interaction value | |

Time from the customers’ last e-commerce consumption to now | |

Current value | Number of e-commerce consumption of customers in the last year |

Total amount spent by customers on e-commerce consumption in the last year | |

Number of customer cross purchases | |

Persistence of customer enterprise relationship | |

Potential value | Customers’ perception of corporate brand image |

Are you willing to recommend others to buy? Customer score | |

Customers’ willingness to become members | |

Number of customer cross-purchases |

Weight setting

The three indicators in the current customer value reflect the different importance of customers to the enterprise. Accurate determination of the weight of each specific indicator plays an important role in customer pre-classification in the current value. At present, the methods to determine the index weight include expert grading method and analytic hierarchy process. In this study, the expert grading method is used to establish the importance of the index, and the corresponding weight set is

Calculate the current value score of each customer.

Through the five-point scoring method, the corresponding numerical values of the three indicators in the current value are known and these numerical values are multiplied by the weight of each indicator that is established by the corresponding expert grading method, respectively. Finally, the current value of the customer can be calculated by adding up, as given the following formula:
_{i}_{i}_{i}_{i}_{R}_{F}_{M}

Pre-classification of e-commerce customers

In this study, the five-point scoring method has been used to establish the scores that customers can obtain for each index. For the sake of simplicity of calculation, customers are pre-divided into five categories, and the higher the score, the greater the current value of customers.

The BP neural network is a multi-layer feedforward neural network, which consists of input layer, hidden layer and output layer [28]. The learning process of the network consists of forward propagation and backward propagation. In the forward propagation, the data pass through the input layer, the hidden layer and the output layer in turn. If the result fails to meet the expected requirements, it will enter the backward propagation, where it distributes the error to each small unit in the network structure, and through constant adjustment, until the output result reaches the expectation [29].

When calculating each node, it needs to use the S-type function for basic calculation, so it requires a hidden layer to solve the problem of decision classification. When there are two hidden layers, the output function can be used on the input image at will. However, for a small network, one hidden layer is enough to complete the work [30].

The actual output is calculated in the direction from input to output, while the weights and thresholds are corrected in the direction from output to input [31].

_{j}

_{ij}

_{i}

_{ki}

_{k}

_{k}

(1) Forward propagation of the signal

Input net_{i} of the

Output _{i}:

Output the input net of the _{k}:

Output

(2) Backward propagation of error

Backward propagation of error, that is, firstly, the output error of neurons in each layer is calculated layer by layer from the output layer, and then the weights and thresholds of each layer are adjusted according to the error gradient descent method, so the final output of the modified network can approach the expected value.

The quadratic error criterion function for each sample _{p}

The total error criterion function of the system for

According to the error gradient descent method, the output layer weight correction Δ_{ki}_{k}_{ij}_{i}

The weight adjustment formula of the output layer:

The output layer threshold adjustment formula:

The weight adjustment formula of the hidden layer:

The hidden layer threshold adjustment formula:

The following formula is finally obtained:

The BP network is a one-way multi-layer feedforward network, which includes input layer, hidden layer and output layer. It is a widely used model at present. The algorithm adopts error backward propagation learning method in the hierarchical network structure, and the learning process consists of forward propagation and error back propagation.

The algorithm of the BP neural network is a kind of learning algorithm that has the characteristics of supervision. The main idea is that for

The three-layer network structure is often used in the research of customer classification in the BP neural network algorithm, so three-layer BP neural network structure is selected to calculate customer value, and the preparatory work includes determining the number of network layers, the number of input layer nodes, the number of output layer nodes, the number of hidden layer nodes and data processing.

In this work, it is found that the research on customer classification only involves the index data at the input level and the measurement of customer value at the output level, and only the BP neural network model with one hidden level can measure customer value, so this study selected the three-layer BP neural network model to measure customer value.

The customer classification index system constructed in this work involves a total of 16 specific indicators, and the benefits that customers can bring to enterprises are calculated according to these indicators, so the number of neurons in the input layer of customer value calculation is 16.

The determination of hidden layers is very significant in BP neural network training, which will affect the final calculation result, but the number of hidden layers is not constant. Generally, the more neurons in the input layer or the output layer, the more complex the network structure will be, and the more neurons in the hidden layer will be needed. Specifically, the number of neurons in the hidden layer to be selected can be determined according to the training results in actual operation.

The relationship between the number of neurons in the hidden layer and the number of neurons in the input layer and output layer in the common three-layer BP neural network model is as follows:

The basis of customer classification in this study is mainly the size of customer value, so in empirical research, the BP neural network is used to calculate customer value, and there is only one output value involved in each sample, that is, customer value, which is expressed by

When training the BP neural network, it is necessary to select certain sample data in advance for training, simulation test and verification, and to normalise the data that have been scored with a five-point system to minimise and maximise, so that the data used for network training are within the range of [0, 1]. The equation used is as follows:
_{i}

Then, the classification model of the e-commerce customer based on the BP neural network is constructed as follows (Figure 5):

After the customer pre-classification processing is completed, half of the customers in each category are randomly sampled as samples for customer classification research, which constitutes a set of data with 260 samples. The reason for further processing is that the samples trained by the BP neural network cannot be too much. Selecting customers from each pre-classification category as sample capacity for training is beneficial to improving the representativeness and balance of samples. Then, the sampled sample data are normalised by minimum and maximum, so that their sizes are all within the range of [0, 1].

The sample data are divided into three categories for training, simulation test and verification of the neural network, while the specific function of the sample is randomly determined by the system. Here, 70% of customer data are taken as the training sample, and the sample size is 182; 15% of customer data are taken as the verification sample, and the sample size is 39; 15% customer data are taken as the test sample, and the sample size is 39. In addition, the number of neurons in the hidden layer is determined; here, it is the default value of 10. Generally, after the default value is selected, the number of neurons can be adjusted according to the actual situation, and different training results can be evaluated, and the number of hidden layers with the smallest error can be selected [32]. Moreover, the number of hidden layers is 6, 7, 8, 9, 10, 11 and 12, respectively. After comparing the mean square error, it is determined that the number of hidden layers is 10. At the same time, according to the network structure diagram, the number of neurons in the input layer is 16 and the number of neurons in the output layer is 1.

Before the neural network training, the maximum training times, the maximum error value and the gradient of the error surface will be set in advance. When one or more indexes reach the set value during the network training, the training will end. Training times is set to the maximum number of iterations, that is, 1000 times, and the final result shows 105 iterations. During the training, the result shows that the training ends in 0.06 seconds, with an initial error of 0.183; at the same time, the initial gradient error of the error surface is 0.368; the maximum number of verification times is 6, and if it exceeds that number, the training will stop, which represents that the training error is greater than the expected error, and the validity verification will stop at once (Table 2).

Training results.

Training time | 0.06 s |

Error | 0.183 |

Gradient of error surface | 0.368 |

Verification times | 6 |

According to the results, the smaller the value of MSE (performance function), the closer the

Fitting evaluation results.

Train | 182 | 1.15322e^{-12} | 9.99999e^{-1} |

Verification | 39 | 2.40519e^{-6} | 9.99985e^{-1} |

Test | 39 | 1.80075e^{-5} | 9.99899e^{-1} |

Figure 6 shows the error convergence of network training, in which the abscissa represents the training times and the ordinate represents the error value. This training converges at the 105th time, stops training and reaches the minimum error value at the 104th time, which converges to 2.4052 × 10^{–6}.

According to the empirical analysis, it can be found that the calculation accuracy of customer value is high. In this study, the trained network has been named net and saved in the workspace of MATLAB software. In practical application, the customer value can be calculated only by using the Subscriber Identity Module (SIM) function [33]. The function of SIM is

Customer value classification results.

Class A customer | [0.75, 1] |

Class B customer | [0.5, 0.75] |

Class C customer | [0.25, 0.5] |

Class D customer | [0, 0.25] |

The concrete result is that the value of customers in class A is the largest, and the value range is within the range of [0.75, 1]. This kind of customers create the greatest benefits for enterprises, and they will actively purchase from the e-commerce platform and may become loyal customers without excessive publicity and promotion. Customers in class B are of great value, and the value range is within the range of [0.5, 0.75]. This kind of customers can also bring great benefits to enterprises, are interested in e-commerce products and have a higher probability of transforming their value into customers in class A, The value of customers in class C is small, and the numerical range is within the range of [0.25, 0.5]. These customers are sceptical about the way of e-commerce consumption, and they are still in the initial stage of understanding the products of the platform, so the input-to-output ratio of enterprises on this customer will not be very large. Customers in class D have the smallest value, and the value range is within the range of [0, 0.25]. This kind of customers do not trust the consumption pattern of e-commerce, and the benefits they can create for enterprises are very limited. Enterprises are advised to give up on them because they have high requirements on products but show little consumption. Even if enterprises invest high resources in customer development, the customer value they can obtain is still very small.

In this study, the BP neural network algorithm is used to classify e-commerce customers. First of all, the customer data of Tmall were obtained by a questionnaire survey, and the data were sorted out and normalised. Secondly, in order to improve the representativeness of the sample, customers were pre-divided into five categories based on the current value data of customers, and half of the customer data from each category were randomly sampled as the sample size of empirical research. Finally, the input and output data of the sample were trained by the BP neural network to calculate the customer value, which was divided into four categories according to the value.

#### Customer value classification results.

Class A customer | [0.75, 1] |

Class B customer | [0.5, 0.75] |

Class C customer | [0.25, 0.5] |

Class D customer | [0, 0.25] |

#### Fitting evaluation results.

Train | 182 | 1.15322e^{-12} |
9.99999e^{-1} |

Verification | 39 | 2.40519e^{-6} |
9.99985e^{-1} |

Test | 39 | 1.80075e^{-5} |
9.99899e^{-1} |

#### Classification index system about e-commerce customer based on customer value.

Customer age | |

Customer income level | |

Customer characteristics of e-commerce | Customer education |

Geographical position | |

Degree of trust | |

Customer interaction value | |

Time from the customers’ last e-commerce consumption to now | |

Current value | Number of e-commerce consumption of customers in the last year |

Total amount spent by customers on e-commerce consumption in the last year | |

Number of customer cross purchases | |

Persistence of customer enterprise relationship | |

Potential value | Customers’ perception of corporate brand image |

Are you willing to recommend others to buy? Customer score | |

Customers’ willingness to become members | |

Number of customer cross-purchases |

#### Training results.

Training time | 0.06 s |

Error | 0.183 |

Gradient of error surface | 0.368 |

Verification times | 6 |

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English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students 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 Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification 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 The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory 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 AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network 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 A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility 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