With the increase in people’s needs along with convenience high technology such as the Internet brings to everyone, there are many risks, such as the security of important data. Nowadays, obtaining secure and important data on the Internet allows businessmen to conduct important business activities and make profits.
The concept of homomorphic encryption was first introduced by Rivest for protecting the privacy of data [1]. Most researchers refer to homomorphic encryption algorithms that support any computational method as fully homomorphic encryption [2], and Dijk
Therefore, in this study, in order to protect the privacy and security of user data in the era of big data, a series of related mature systems are developed using homomorphic encryption algorithms, and encryption machines are realised using homomorphic encryption schemes, which are combined with big data technology to avoid the problem of deepening of circuits and the inability to decrypt them correctly. To provide users with more peace of mind and a more secure big data environment, to carry out important business activities, profit for businesses and more scientific formulation of accurate marketing strategies.
Homomorphic encryption is a technique that encrypts data through processing to achieve confidentiality. In the homomorphic encryption algorithm, the homomorphic ciphertext is obtained immediately after encrypting the data using public and private keys to operate on the ciphertext, and the direct result of its decryption operation is used to encrypt the data explicitly again, and the decryption result is the same. Homomorphic encryption can prevent the leakage of personal data and enable data sharing under the premise of privacy protection based on the characteristics of multisource cooperative computing [9]. Figure 1 shows the basic process of homomorphic encryption.
Let the encryption algorithm be
For a valid algorithm ⊙, if
There are altogether three different algorithms for homomorphic encryption, namely, additive homomorphism, multiplicative homomorphism and hybrid multiplicative homomorphism [10, 11].
When
When
When
In the process of using homomorphic encryption, it is necessary to use vectors as the basis before starting the computation, so vector homomorphic encryption scheme is indispensable for picking and choosing [12]. Before the integer vector homomorphic encryption scheme, there are many scholars who put forward their views on integer vector encryption homomorphism. Among them, VHR stands out among these schemes [13–16].
Much homomorphic encryption of integers is achieved by bitbybit encryption schemes to achieve full homomorphic encryption, which are difficult to implement in practical applications due to their extremely low efficiency. VHE schemes, although unable to achieve full homomorphism, only need to satisfy the required operation and depth, which have high efficiency and can be more widely used in practice [17].
To understand the partial homomorphic encryption VHE algorithm, it is necessary to first understand some basic notation descriptions [18–21], as shown in Table 1.
Symbol description
Λ  Securitylevel parameters 
Bitisation parameters  
Large prime numbers that satisfy  
Vector dimension of the explicit text  
Vector dimension of the ciphertext  
Gaussian distribution  
W  Large integer, w ≠ 0 
Obeying Gaussian distribution of noise  
Finite fields on  
An integer vector  
The unit matrix of  
The unit matrix of  
Required parameters for the private key  
[  The nearest integer of 
[  The nearest integer after the modulo 
Initialisation stage
Given the securitylevel parameter
Select distributions
Choose the Gaussian distribution
Publish the public parameters at Param = (m,n,p,q,w,χ).
Generate key stage
Generate two matrices
Generate two matrices: the key matrix
Calculate the key
Ensure the Sprivacy of the key and publish the public key M.
Encryption stage
Select the appropriate noise e ← χ^{n}.
Compute the ciphertext
Output the cipher text to
The whole encryption process is shown in Figure 2.
Decryption stage
Compute
Output plaintext at
The correctness of the decryption is guaranteed by the formula
In practical applications, a certain number is often increased as the homomorphic computation proceeds, and when that number is large enough, it will lead to decryption failure. Therefore, in practical applications, we can obtain the depth of homomorphic computation that a ciphertext can perform from the relationship given in the previous formula and then limit it in the application to ensure that the result of homomorphic computation can be decrypted smoothly.
The VHE scheme converts the integer data into vectors and then encrypts them homomorphically, while the key conversion technique plays a key role in the encryption scheme. The key conversion technique guarantees the correctness of decryption by converting the original key and ciphertext pair
In the encryption phase, let the initial key matrix be
To verify the correctness of the encryption, for the plaintext
Transform the original key and cipher
Similarly, all elements
Since vectors perform the bitwise operation and matrices perform the inverse operation, we can conclude that
Convert the intermediate key
Construct the key transformation matrix
The previous equation holds when the new key
The relationship equation is obtained as follows:
The vector homomorphic encryption scheme VHE supports three basic homomorphic operations, namely, the homomorphic linear transformation operation, the homomorphic addition operation and the homomorphic weighted inner product operation. In practice, many other operations can be converted to a combination of these operations. Since we found in our practical study that the weighted inner product operation can be replaced by using the linear transformation operation, we drop the weighted inner product operation in our study, so we only introduce the two basic homomorphic operations next.
Choose two plaintext vectors
The entire equation can be written as follows:
From the equation, we can see that by directly doing the addition operation on the ciphertext, we can get the ciphertext corresponding to the ciphertext domain. So, the scheme satisfies the additive homomorphic operation of vectors.
Given a plaintext vector
We can think of
The relevant machine learning algorithms covered in this thesis do not use the weighted inner product operation. Therefore, this article does not give much description of the weighted inner product operation [28–31].
In the Internet and Internet of Things era where technology empowers life, and with the Chinese government encouraging the development of the real economy, online consumption is still the choice of half of us. With the increase of Internet penetration, online consumption forms are on the rise and have a great tendency to cover the whole Chinese market. Therefore, while the online economy is developing at a high speed and bringing convenience to consumers, the possible risks of the online market should also be improved to provide protection for consumers.
In response to this problem, which is also considered in the context of the advantages and disadvantages specific to big data, five main problems are faced [31–34]:
(A) Personal privacy protection  (B) Crossborder data flow 
(C) Traditional security measures are difficult to adapt  (D) Platform security mechanisms await improvement, leading to weak security guarantees such as user identification and authorised access 
(E) Application access control is becoming more complex 
In business activities, this problem is more serious for the sake of selfinterest of each enterprise. Big data allows deeper calculation and analysis of consumption data, which can make the development of marketing strategies more scientific. Usually, enterprises use machine algorithms and program settings to count and analyse users’ consumption behaviour, and classify customers according to their consumption behaviour so as to achieve personalised pushing of marketing contents. However, to ensure the accuracy of the machine for big data analysis, a huge amount of data is needed. Driven by economic interests, consumers’ personal information and consumption records are illegally collected, stored, used, or even sold, which not only violates personal privacy but also brings the risk of personal and property damage to consumers. For the sake of consumer information security, how to safely collect and use these data is a problem to be solved. The homomorphic encryption allows the processing of encrypted ciphertext, which can ensure both the security of data processing, that is the original data will not be leaked when processing ciphertext data, and the correct decryption, that is, the user who has the private key can decrypt the processed data and get the correct arithmetic result.
After analysing the characteristic requirements for secure sharing of consumer data, and considering the requirements for privacy in sharing consumer data and conducting precision marketing to consumers, the solution should meet the following design objectives:
(A) Data validity  To be able to ensure that its hedge data are authentic and trustworthy, a strict authentication mechanism is needed to ensure that only legitimate identities can log in to the system and share user consumption data, preventing other malicious competitors from participating in the data sharing. 
(B) Data confidentiality  The purpose of the solution is to ensure the privacy of customer consumption data, which must be kept confidential when uploaded by the mall, and also during data processing. 
(C) Correctness of results  The correct processing of multiclient data is a fundamental requirement for financial data sharing solutions, which must be designed to ensure the correctness of data clustering results. 
(D) High efficiency  The solution requires the use of efficient homomorphic encryption algorithms and clustering algorithms as a way to ensure the efficiency and practicality of sharing consumer data and performing accurate marketing. 
(E) To achieve precision marketing  In order to differentiate marketing based on different customer groups, tap the potential value of customers and maximise profits, we need to analyse the basic information, behavioural information and consumption data of consumers to segment customers and further realise precise marketing. 
It is according to the customer’s value, needs and consumption preferences to gather similar customers into groups, enterprises and businesses, and then according to the results of customer segmentation to provide targeted products, services or marketing for different groups of customers so that both sides can benefit from it.
The key to winning in consumer market competition lies in the grasp of market demand and customer characteristics, while customer segmentation can play the following roles in market competition:
Customer identification and positioning. Due to the differences in the living environment and consumption level, there is a diversity of consumer needs, so merchants can realise the grasp of different customer needs through segmentation, discover the potential needs of a certain target consumer group and then launch targeted products and services.
Market analysis and grasp. Since the consumption habits and levels of consumers are roughly constant, segmentation can assess the current and potential value of customers from the perspective of market analysis. For some merchants, customer segmentation based on big data can be used to locate customers who can bring greater benefits as well as those who bring less benefits, which is beneficial to adopt different marketing strategies.
The ultimate purpose of customer segmentation is to enable merchants to differentiate marketing for different customer groups, to tap the potential value of customers and maximise profits, to more precisely select the highquality customers who can bring high revenue to the merchant among a large number of consumers according to the positioning of each merchant’s products and to quickly select the consumer customers who can sustain attention.
Customer segmentation usually takes the interval, frequency and amount of consumption behaviour as criteria, but the two variables of consumption times and total consumption amount in the same time period have multicollinearity, so this article deforms the total consumption amount into the average consumption amount. Since the consumption data comes from the same mall, the mall backend can get the average consumption amount by aggregating the consumption records according to the consumer’s member id, and the data can be tracked and recorded several times, which is beneficial for merchants to retrieve the average consumption amount in different time periods according to different needs, and data are reliable and targeted.
In recent years, the ecommerce industry has shown rapid development, people’s frequency of consumption in shopping malls has dropped significantly, while the number of physical stores is basically saturated. In this context, the physical stores on the characteristics of customers and the actual needs of a deep grasp is the key to compete for the consumer market, to potential customers to carry out different attractive activities, the implementation of targeted marketing programs for old customers, for different customer groups Introduce package services that better meet the customer needs. To achieve those mentioned before, a comprehensive and detailed segmentation of customer groups is necessary.
In order to maximise the analysis and utilisation of consumption data, the data owner (mall) needs to provide consumption data generated in all stores of his mall, but to ensure the privacy of the information, the consumption data should be homomorphically encrypted in the system before sharing the consumption data; in order to enable the data user (a merchant who needs to send marketing SMS) to conduct personalised marketing to all consumers in the mall according to the characteristics of his own products. To attract specific users or tap potential users, merchants can propose the required number of customer categories and corresponding marketing SMS in the system; the thirdparty computing center, based on the encrypted consumption data provided and the required number of customer categories
Big data analysis of the data: After analysis is completed and the results are returned to the system database, advertising operators can view the classification results of user consumption data, set different SMS templates according to the user’s cell phone number and the corresponding marketing SMS and finally send SMS in bulk.
In summary, the solution includes four participating entities: the consumer data owner (the mall), the consumer data user (a particular merchant that needs to be marketed), the thirdparty computing centre and the advertising operator. The general framework of the solution is shown in Figure 4.
In this solution, although the data owner (shopping mall) owns all the registration information and consumption records of consumers, the consumption data are encrypted into cipher text in the system and then uploaded, which ensures the security of the data from the source. The thirdparty computing centre retrieves the cipher text from the database but does not have access to the real consumption data. When a merchant needs to send marketing SMS, the required number of customers and the corresponding marketing templates are entered in the system, and after the thirdparty computing centre classifies the customers according to the demand, only the merchant has the right to view the customer classification in the system, and the system automatically anonymises the personal information of consumers, such as phone numbers, so that the merchant cannot obtain personal information for private marketing, which ensures the privacy and security of consumers. The advertising operator reads the data and SMS that need to be analysed preset by the merchant from the system, and sets the corresponding marketing SMS according to the classification result. According to the classification results, the corresponding marketing SMS is set, and then the SMS is sent in batch with one key, without touching sensitive information, such as phone numbers, which not only ensures no leakage of consumer information but also enables accurate marketing to different consumer groups.
The main steps of a precision marketing program based on consumer data and homomorphic encryption algorithms include the following:
The data owner (mall) downloads the consumer data upload template and imports the user data into the template according to the specifications.
In the data management of the consumption data encryption system, user consumption data for a certain time period are encrypted and uploaded to the database for use by advertising operators and thirdparty computing centres.
The advertising operator sets the value of
A thirdparty computing centre reads the dataset, performs big data processing on the ciphertext according to
Based on the generated customer classification results and the specific marketing SMS provided by the merchant, the advertising operator sets the corresponding marketing SMS in the marketable list and sends them.
The original homomorphic encryption (including VHE) scheme only supports integer calculation, but the big data algorithm needs to perform averaging operation in order to compensate in this drawback, which may lead to the generation of floating point numbers, resulting in the lack of precision of the obtained data; the indicators related to the amount in this scheme may involve decimals, and the accuracy of the results will also be affected if the decimal places are discarded, so the direct use of the VHE encryption scheme is not applicable to this scheme.
To address the aforementioned problem, this study extends the data range of the algorithm to the fractional range. The algorithm is improved by recording the number of decimal places
The correct plaintext data are obtained by converting “number” to “decimal”.
The specific steps for complete VHE encryption are as follows.
Record the number of decimal places n and transform the “decimal” into “integer” by multiplying the original text by 10% and shifting the decimal point to the right by n places; the transformed “integer” is then homomorphically encrypted and calculated. When decrypting the data, the “integer” is converted to “decimal” by shifting n decimal places to the left to ensure the correctness of the encryption.
The original key S and ciphertext pair c is bitwise processed according to Eq. (11) to obtain the intermediate key ciphertext { S_{*}, c_{*}}.
Convert the intermediate key S_{*} ∈ Z (×%: to the target key matrix S8 ∈ Z, (×%8; and introducing noise E and random integers matrix A, and construct the key transformation matrix M ∈ Z% according to Eq. (13).
Encryption of the consumption data using the new key matrix S8 and the key transformation matrix M to ensure that c8 = Mc_{*}, that is, the ciphertext is equal to the key transformation matrix multiplied by the intermediate ciphertext, which guarantees the correctness of the encryption.
After the encryption is completed, the cipher text is stored in the database; the aforementioned process for decimal data is for single data, while in the actual calculation process, each data may not have the same number of decimal places n. Therefore, it is necessary to unify the number of decimal places n to avoid the phenomenon of misplaced summation during calculation. Since the consumption amount is only dollars, cents and angles, the number of decimal places of decimal data does not exceed 2. In practical application, the number of decimal places n = 2 is specified, and less than n places are made up by 0 to facilitate calculation, and the format of shared data is also unified to facilitate data storage.
The biggest change in the digital era is the ability to collect various data from consumers through big data, such as shopping preferences and payment data. While collecting data, the data will be homomorphically encrypted, and the encrypted data will be stored using big data technology to protect user privacy. The collected data and calculated metrics form the user profile of big data, and the integration of these technical tools with marketing thinking is the biggest change in the digital era [35]. Users are categorised through the “Data Management” module of the Big Data platform, and target customers are classified.
The means of reaching consumers have changed in the digital era, such as AR, VR, social media, APP, search, smart recommendations, O2O, DSP and various other means of reaching [36, 37]. Through various means of reach, companies collect consumer information anytime and anywhere, and encrypt and upload these user consumption data to a database for use by advertising operators and thirdparty computing centres. Users have unique user names and passwords. The operator management interface, through the role management module and the permission management module, grants the relevant administrator permissions before accessing the data information in the system.
The establishment of many communities ensures that companies can directly connect, interact and engage with their customers in a “disintermediated” context. Operators can set
Marketing is not only an investment, it is also something that can yield a direct return. Companies build communities and absorb brand fans into their ecommerce platforms, or among the pages of databased platforms. Customers are monitored through homomorphic encrypted data, and information on customer preferences, psychological changes and spending power is analysed in the use of big data [38]. Immediately after that, companies can identify the characteristic people and provide the products they need according to the homomorphic encryption algorithm to purposefully stimulate consumption and realise transactions.
In the digital age, the most important feature of brand marketing is that consumers are gradually becoming part of the enterprise, using data intelligence to do consumer operations – “‘insight into consumer psychology”’, “‘influence consumer behaviour’“ and “‘measuring consumer change”’, to achieve dataenabled consumer operations. That is to say, our companies can only go far with consumercentric, accurate value proposition and reshaped marketing model [39–41].
The combination and application of big data and homomorphic encryption in the offline consumer market makes the formulation of marketing strategies more scientific, using homomorphic encryption algorithms to protect the data transmitted by users, and big data analysis technology to count and analyse the acquired data and classify customers according to their consumption behaviour, so as to realise personalised pushing of marketing contents. The big data analysis needs massive data as the basis, and there are many unscrupulous merchants in the market who obtain consumer data for their own interests and harm the rights and interests of consumers. This article integrates homomorphic encryption algorithm into the big data platform and encrypts the home user data, which well protects the privacy and security of consumer data.
The specific findings of this study are as follows.
Complete the design of the precision marketing scheme based on consumption data and homomorphic encryption algorithm. Introduce homomorphic encryption into the consumption data sharing, combine with big data analysis technology and carry out detailed design of the accurate marketing scheme based on consumption data and homomorphic encryption algorithm. The data owner encrypts the consumption data into cipher text before uploading, which ensures the security of the data from the source; the thirdparty computing centre retrieves the cipher text from the database without touching the real consumption data; the data user only restricts the permission in the system, and the system automatically anonymises the personal information of consumers, which ensures the privacy and security of consumers.
An empirical study of the improved algorithm was completed.
Through experiments, the effects of different variables, such as the number of plaintext bits, the number of ciphertext bits, the amount of data and the number of clusters k, on the encryption efficiency of the improved algorithm and the efficiency of the big data algorithm are compared. The improved homomorphic encryption algorithm and the improved big data analysis technique are stable, secure and efficient, and can achieve the requirements of this scheme.
A user data encryption analysis system designed in a precision marketing program based on consumer data and homomorphic encryption algorithms was implemented.
The system development is based on Springboot using Spring + SpringMVC + MyBatis framework technology, which conforms to the fourtier architecture system of Java EE development standards, and stores data in MySQL database. The test results of the system show that the system achieves login, authentication, and the main functions of the four participating entities in the scheme design, proving that the system meets the expected design goals of the scheme in terms of data validity, data confidentiality, correctness of results, efficiency and the ability to achieve accurate marketing.
(A) Data validity  To be able to ensure that its hedge data are authentic and trustworthy, a strict authentication mechanism is needed to ensure that only legitimate identities can log in to the system and share user consumption data, preventing other malicious competitors from participating in the data sharing. 
(B) Data confidentiality  The purpose of the solution is to ensure the privacy of customer consumption data, which must be kept confidential when uploaded by the mall, and also during data processing. 
(C) Correctness of results  The correct processing of multiclient data is a fundamental requirement for financial data sharing solutions, which must be designed to ensure the correctness of data clustering results. 
(D) High efficiency  The solution requires the use of efficient homomorphic encryption algorithms and clustering algorithms as a way to ensure the efficiency and practicality of sharing consumer data and performing accurate marketing. 
(E) To achieve precision marketing  In order to differentiate marketing based on different customer groups, tap the potential value of customers and maximise profits, we need to analyse the basic information, behavioural information and consumption data of consumers to segment customers and further realise precise marketing. 
Symbol description
Λ  Securitylevel parameters 
Bitisation parameters  
Large prime numbers that satisfy 

Vector dimension of the explicit text  
Vector dimension of the ciphertext  
Gaussian distribution  
W  Large integer, w ≠ 0 
Obeying Gaussian distribution of noise  
Finite fields on 

An integer vector 

The unit matrix of 

The unit matrix of 

Required parameters for the private key  
[ 
The nearest integer of 
[ 
The nearest integer after the modulo 
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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 frontline city administrative lawenforcing 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 Nonlinear 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 nonlinear visual matching model under inherent constraints of images Good congruences on weakly Uabundant 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 multisource heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listedcompanies in the automobile manufacturing industry Research on design of customer portrait system for Ecommerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language FedUserPro: A user profile construction method based on federated learning A multifactor Regression Equationbased 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 Multifeature 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 FirstOrder 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 EnglishChinese CrossLanguage 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 horizontaltorsional 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 crossborder Ecommerce platform based on the combined model A mathematical model of PCNN for image fusion with nonsampled contourlet transform Nonlinear Differential Equations in ComputerAided 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 DiamondSquare 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 Crossborder Ecommerce 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 Timedelay 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 watersaving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of AirConditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the winlose 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 ecommerce 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 Crossborder Ecommerce 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 ecommerce 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 ecommerce 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 smoothnessinformed 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 Crossborder Ecommerce 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 ELECTRABiLSTMCRF 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 ChineseEnglish Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithmbased congestion control optimisation for mobile data network