This article applies mathematical probability theory to statistical algorithms to conduct game analysis on the relevant marketing decisions of foreign trade cross-border e-commerce. We build a theoretical framework for the collaborative development of SMEs and cross-border e-commerce platforms. At the same time, build a trustworthy transaction margin mechanism for cross-border e-commerce transactions in a fuzzy market environment. The participation of the blockchain big data platform can promote the development of foreign trade cross-border e-commerce toward a more transparent and healthy partnership.

#### Keywords

- Cross-border e-commerce
- Probability theory statistics
- Evolutionary game
- Enterprise marketing

#### MSC 2010

- 91A80

Before the New Deal, cross-border e-commerce bonded imports were implemented as a “negative list.”. Commodities already in transit but not on the list have been stranded at the terminal and airport. These have brought huge losses to cross-border e-commerce companies [1]. If the business owner predicts that the relevant regulatory authorities will continue to improve, it will increase the stocking of goods not on the positive list. This leads to a monopoly of “people without me.” Therefore, there will be a three-stage game from stocking to sales: In the first stage, there is a game of “stocking” and “supervision” between the company and the government. The second stage is that after the company has decided, there will be a network of strategies of multiple companies in the market. This article assumes that one company has adopted a strategy of stocking products other than the “positive list” to form a monopoly in the cross-border e-commerce market. Another company can only stock and sell products using traditional trading methods. This forms competition with its sales channels. The third stage is the pricing strategy of the sellers of the two channels in the market when facing rational consumers [2]. This strategy maximizes self-interest. The relevant suggestions put forward by this article through the three-stage game analysis between the government, enterprises, and consumers are more theoretical and practical.

Promoting the steady and healthy development of the cross-border e-commerce industry while meeting regulatory requirements and preventing and controlling risks is a crucial matter. This puts forward higher regulatory requirements for relevant regulatory agencies such as customs, taxation, and national inspection. The introduction of the “positive list” is a manifestation of increased supervision. From the relationship between relevant regulatory agencies and cross-border e-commerce companies, companies will always pursue excess profits and increase their supply types in the short term. In this way, the monopoly situation of “people without me” is realized. The government has stepped up supervision to prevent the risks of moving too fast. This reduces the profit margins of cross-border e-commerce companies [3]. When the government gradually enriches the positive list, cross-border e-commerce companies will start a new round of stocking decisions for products not on the positive list. The two sides promote each other in a dynamic game.

The subjects of the game are cross-border e-commerce companies and related regulatory agencies. The enterprise's decision strategy set is {stocking, not stocking}. The regulatory agency's decision-making strategy set is {included in the list, not included in the list}. Cross-border e-commerce companies normally stock up to obtain normal income _{E}_{1} and pay the cost _{E}_{1}. Relevant regulators who choose to be included in the list will obtain benefits _{M}_{1} and pay costs _{M}_{1}. When the company stocks goods out of the list and the regulator does not supervise it, the company obtains an excess income _{E}_{2}, pays a cost _{E}_{2}, and the regulator assumes the risk _{M}_{2}. In the case of not being included in the list by the supervisory authority, it will obtain income _{M}_{2}. At the same time, if the company adopts stocking, the regulatory agency will obtain additional penalty income _{M}_{3} and bear the cost _{M}_{3}. The combination of the game process is as follows:

When a company chooses not to stock products not on the positive list, the regulator adopts the income function of the two parties when they are included in the list as:

The company adopts the inventory strategy for the products outside the positive list, and the supervisory agency adopts the listing strategy. The income functions of the two parties at this time are:

The enterprise adopts the non-stocking of the goods outside the positive list, and the supervisory agency adopts the non-listed list. The profit function of both parties is

The company adopts the strategy of not being included in the list when the company adopts the stocking of goods that are not on the positive list. The profit function of both parties is

In the game process, cross-border e-commerce companies adopt non-stocking and stocking strategies with a probability of 1-a, respectively [4]. The regulatory agency adopts the listing and non-listing strategies with the probability of b and 1-b. The income matrix of regulatory agencies and cross-border e-commerce companies is shown in Table 1.

Revenue matrix of cross-border e-commerce companies and related regulatory agencies

Regulatory Authority | |||
---|---|---|---|

Included in the list (b) | Not included in the list (1-b) | ||

Not stocking (a) | (IE1-CE1, IM1-CM1) | (IE1-CE1, IM2-CM1) | |

Stocking (1-a) | (IE1+IE2-CE1-CE2, IM1-CM1-CM2) | (IE1-CE1-CE2-IM3, IM2+IM3-CM1-CM3) |

The income of cross-border e-commerce companies adopting pure non-stocking and pure stocking strategies is

Assuming each participant's bounded rationality and F(a)=0, the fixed point of the replicated dynamic equation can be solved. We get the dynamic replication equation of cross-border e-commerce companies

Assume that

Distribution of equilibrium points of dynamic equations

Det(J) | Tr(J) symbol | Result | |
---|---|---|---|

+ | + | Unstable point | |

+ | − | ESS | |

− | + | ESS | |

− | − | Unstable point | |

− | 0 | Saddle point |

From Figure 1, we can see that the evolutionary stable equilibrium points in the dynamic evolutionary game between cross-border e-commerce companies and relevant regulatory agencies are

From the perspective of the long-term and healthy development of cross-border e-commerce, the probability that relevant regulatory agencies will be included in the positive list is as follows:

The above formula shows that the difference between the public opinion pressure of the relevant regulatory agency choosing not to be included in the positive list and the decline in reputation caused by the inclusion of the positive list is _{M}_{3} − _{M}_{2} less than the penalty income _{M}_{3} when not included in the positive list
_{M}_{3} − _{M}_{2} = _{M}_{3} − _{M}_{3}.

The greater the penalty income, the greater the probability of not being included in the positive list. When
_{M}_{3} − _{M}_{2}. The smaller the public opinion pressure of not being included in the positive list, the greater the reputational impact of being included in the positive list and the greater the probability of not being included in the positive list.

When
_{M}_{2}. The greater the probability that cross-border e-commerce companies choose to stock up. When
_{E}_{1} is inversely proportional. The smaller the cost of stocking, the greater the probability that cross-border e-commerce companies will choose to stock.

Conclusion 1: The stocking probability of an enterprise is directly proportional to the excess income, and it is inversely proportional to the stocking cost. The probability that a regulatory agency chooses to monitor is directly proportional to the penalty income. It is inversely proportional to the pressure of public opinion not included in the list. It is directly proportional to the reputation impact of the list.

Under the condition that the government allows the sale of off-list goods, enterprises are automatically divided into two teams with an out-of-stock strategy due to stocking and not stock. Enterprise 1 can only purchase goods through traditional trading methods and sell them through traditional retail channels [7]. Enterprise 2 can stock up and sell on cross-border e-commerce channels and traditional trade channels. At this stage, this article makes the following assumptions:

The market is a supply chain system composed of a cross-border e-commerce channel sales company and a traditional retail channel sales company.

The two companies pursue their profit maximization through price competition.

Two companies sell the same product, and the product itself is completely replaceable.

Each company has its own fixed loyal consumers. There are still a group of consumers in the market who are pursuing low prices.

In this stage, the Bertrand model is used to characterize the competition among enterprises. Let _{ue}_{ut}_{ue}_{ut}_{ci}_{ti}_{e}_{2} represents the sales price of enterprise 2 in the cross-border e-commerce channel. It is assumed here that the price influence of the commodity itself is greater than the mutual influence. Then the demand function faced by enterprise 1 can be expressed as follows:

The demand function faced by enterprise 2 in traditional trade sales channels can be expressed as follows:

The demand function faced by enterprise 2 in cross-border e-commerce sales channels can be expressed as follows:

Among them, _{1}, _{t}_{2}, _{e}_{2} represents the potential market size of companies 1 and 2 in their respective sales channels. _{1} represents the degree of substitution of two companies in traditional sales channels. _{2} represents the degree of substitution between traditional sales channels and cross-border e-commerce sales channels. Therefore, the profit function of enterprises 1 and 2 can be expressed as follows:

Conclusion 2: The equilibrium price strategy of the Bertrand game between firm 1 and firm 2 is

Prove that: _{1} and _{2} are equal to 0 when the partial derivative of _{t}_{1}, _{t}_{2}, _{e}_{2}, is equal to 0.

So we can get

Combine the above formula to get:

Assume

Since the sum of the modules of the non-diagonal elements in each row of _{1} is less than the module of the diagonal elements in this row, _{1} is the diagonal dominance matrix. In this way, we can easily obtain that _{1} is a non-singular positive definite matrix [8]. Therefore, the equilibrium price strategy

Corollary 1: When companies 1 and 2 play the Bertrand game, the proof of

In the supply chain of traditional trade channels, since commodities are substitutable, their demand elasticity is relatively large. Due to the low cost of cross-border e-commerce stocking channels, enterprise 2 chooses to cut prices in cross-border e-commerce stocking channels to gain market share [9]. At this time, enterprise 1, with only one stocking channel, chooses the price reduction strategy. Enterprise 2 chooses to reduce the price simultaneously. Therefore, it can be seen that after the introduction of the positive list, the prices of some products that are not on the positive list (such as the Kao steam eye mask) will have a certain degree of price reduction in supermarkets. This is to resist the advantages of cross-border e-commerce in stocking sales before and after introducing the positive list. Due to the monopoly of cross-border e-commerce stocking channels, price demand elasticity is small. When the demand elasticity of cross-border e-commerce stocking channels increases, Enterprise 2 can only use traditional trade stocking imports for products that are not on the positive list. There are still some consumers in the market who are keen to sell products through cross-border e-commerce stocking channels. The decline in the supply of this channel has caused Enterprise 2 to increase its profits by increasing prices. As the monopoly advantage of cross-border e-commerce stocking channels is gradually disappearing, in order to maintain market share, enterprises 2 have to adopt a strategy of lowering prices in traditional trade stocking sales.

Corollary 2:

Due to the substitutability of products and the greater flexibility of alternative channels, cross-border e-commerce stocking channels have to increase prices to maintain profit margins after the tax reform [10]. Corresponding enterprise 2 will keep the price advantage of cross-border e-commerce stocking channels in the minds of consumers, and will also increase prices correspondingly in traditional trade stocking channels. As a market follower, Enterprise 1 also raises prices to increase profits.

Conclusion 3: There is the following relationship
_{1}, _{t}_{2}, _{e}_{2}.

Prove:

Since the channel is not dominant, the demand of enterprise 1 is greatly affected by the price in the competition with enterprise 2, so at this time, the price and demand decrease at the same time, which leads to a decrease in profit. When the demand elasticity of cross-border e-commerce stocking channels increases, enterprise 1 seizes the opportunity to choose to reduce prices and increase market share at this time, which will lead to increased demand and profit recovery.

Corollary 3: There is the following relationship
_{1}, _{t}_{2}, _{e}_{2}.

Prove:

Since the demand of enterprise 1 in the competition with enterprise 2 is greatly affected by price, when enterprise 1 chooses to reduce the price, enterprise 2 will also choose to reduce the price. Because enterprise 1 has some loyal customers, in the price game, enterprise 2's demand and profit decrease when facing the market demand of enterprise 1. However, the dual stocking channels of enterprise 2 enable enterprise 2 to have an advantage in the Bertrand game with enterprise 1. The demand market for traditional trade stocking channels faced by enterprise 2 is greater than that of enterprise 1. Profits of traditional trade stocking channels have risen. As sales progress, more companies adopt traditional trade to enter the market, which increases the elasticity of demand in the traditional trade market [11]. Enterprise 2 adopts a price reduction strategy to compete with Enterprise 1 completely Bertrand, achieving Bertrand equilibrium in price competition. This will lead to reduced profits. Corollary 1 shows that the existence of consumers who have a soft spot for cross-border e-commerce stocking channels makes enterprise 2 raise prices in cross-border e-commerce channels. However, due to the decrease in demand, profits will fall sharply.

In the second stage of Bertrand competition, this article only considers one commodity. Because this product is completely replaceable, the competition is only channel competition. In actual competition, companies often take the complementary cooperation between commodities and channels and complement each other to occupy the market. In this stage, this article considers that enterprise 1 uses complementary products to improve its competitiveness. Then the demand function faced by enterprise 1 for product A under the traditional trade stocking mode can be expressed as follows:

The demand function faced by enterprise 1 for product B under the traditional trade stocking mode can be expressed as follows:

The demand function faced by enterprise 2 for product A under the traditional trade stocking model can be expressed as follows:

The demand function faced by enterprise 2 for product A in the cross-border e-commerce stocking mode can be expressed as follows:

Among them,

Conclusion 4: The equilibrium price strategy of the Bertrand game between firm 1 and firm 2 is

Corollary4:

Since the complementary commodity B has just entered the market and its demand elasticity is small, enterprise 1 will choose to increase the price in order to occupy the market to obtain excess profits. At the same time, company 1 will lower the price of commodity A as a bait to increase sales profits. Due to the competitive relationship of commodity A, enterprise 2 will respond to the price reduction in a timely manner. During the Bertrand game of price reduction between the two parties, the elasticity of demand for commodity A gradually increases. Since enterprise 1 uses complementary product B to occupy the market, it will use the bundling strategy to increase the prices of products A and B at the same time. When the demand elasticity of the cross-border e-commerce sales channel of commodity A increases, enterprise 1 will reduce the price to counter enterprise 2. At the same time, enterprise 1 still chooses to increase the price of commodity B as a supplement to the reduced profit of commodity A. Similarly, Enterprise 2 will also respond to price cuts in traditional channels. It will use cross-border e-commerce channels to increase prices to supplement profits.

This article establishes a three-stage game in the process of an import and export trade enterprise's transformation to cross-border e-commerce. We use the Bertrand game model to analyze the channel price game with market competitors in the second stage after the effect of the first stage is reached. The article makes certain theoretical suggestions for enterprises to rationally price in order to obtain high profits. Traditional trade stocking channels use the introduction of complementary products as a strategy to counter cross-border e-commerce stocking channels. Similarly, we use Bertrand game to analyze the pricing strategy of enterprises in the game process.

#### Distribution of equilibrium points of dynamic equations

Det(J) | Tr(J) symbol | Result | |
---|---|---|---|

+ | + | Unstable point | |

+ | − | ESS | |

− | + | ESS | |

− | − | Unstable point | |

− | 0 | Saddle point |

#### Revenue matrix of cross-border e-commerce companies and related regulatory agencies

Regulatory Authority | |||
---|---|---|---|

Included in the list (b) | Not included in the list (1-b) | ||

Not stocking (a) | (IE1-CE1, IM1-CM1) | (IE1-CE1, IM2-CM1) | |

Stocking (1-a) | (IE1+IE2-CE1-CE2, IM1-CM1-CM2) | (IE1-CE1-CE2-IM3, IM2+IM3-CM1-CM3) |

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