With the continuous development of the economy, people's living standards are steadily improving, and the demand for education is increasing, tennis is popular as a fashionable and recreational activity. However, the traditional teaching mode is inefficient and lacks systematization and completeness, which affects the effectiveness of classroom teaching and causes a series of problems. In order to solve these problems, this paper designs a tennis mobile support system in the mode of teaching assistance, which aims to improve the efficiency of the classroom and increase the interest of students. The software uses web-based technology and web platform for database management and data interaction. In the development process, the main control module, control functions and other related variables are written in B/S programming language[1]. At the same time, we use Java language to build the model to realize the functions, and finally combine each sub-entity into a complete application, and compare and summarize the effect of classroom learning with the traditional teaching mode[2].

In foreign countries, in the early 1970s, multimedia classrooms were introduced in physical education in some universities. This not only provides convenience for students but also brings a lot of convenience for school management and publicity and education. With the rapid spread of information technology such as Internet technology and computer network communication technology and the expansion of application fields, these network technologies have transformed and upgraded the traditional classroom model[3]. More and more colleges and universities are considering this new form of multimedia classroom when building their own teaching platform, and assistive teaching is also one of the very important research areas. Based on the design of mobile multimedia classroom, the basic information, video and user registration functions of the tennis auxiliary system are implemented to provide students with a convenient way to learn[4,5].

With the development of the Internet, mobile video teaching is also gradually emerging. One of the common denominators is the use of web technology. The design of tennis assistance systems through the Internet is mainly through the database to achieve the exchange of information, data and other interactive functions, and it can analyze and organize these contents, so as to come up with solutions for users to use as a reference basis to achieve better results[6]. Another significant feature is that the software can provide services anytime and anywhere in real time and sharing, which creates possible conditions for users to communicate with each other and learn through the software, thus improving the utilization of information and facilitating the tennis sports assistance system[7,8]. Therefore, this paper is based on the design of some common problems in mobile video-assisted teaching.

javaSwing technology: it is a new technology popular in recent years, its main function is to provide some query and browsing services, through this system can realize a lot of course information, video materials and other related content. The use of this technology in tennis teaching can better help students improve their learning efficiency. javaSwing technology structure is shown in Figure 1.

solidworks development tools: solidworks is a general-purpose software, which can help users to provide a lot of practical, convenient and powerful tools, it is very convenient to use. This paper focuses on a solidworks-based tennis assistance system, which uses Myeclipse as the development tool and a variety of modular methods to achieve simple functional operation of each sub-module.

B/S structure: B/S structure is a database technology-based, process-oriented and object engineering system, whose structure is shown in Figure 2. It has two main types: one is to process the data directly, and the other is to analyze the data interactively, which is also called parallel type[9]. In this auxiliary management system, MySQL is used as the backend database to store information resources and support the operation of various functional modules, while for the user needs a powerful and easy-to-use tool, the B/S structure system can well meet the user requirements to implement and manage the process.

Database technology: Database technology is a data-based processing technology that provides the user with the required information by means of storage and calculation, as well as analysis and query. A large amount of original credential information is needed in the tennis sports assistance system, and the saving of relevant records can be completed when the parameters are entered. The data storage process is shown in Figure 3.

ASP.NET technology: ASP technology is a new type of online programming software, whose structure is shown in Figure 4. It is combined with traditional computer, it has powerful functional modularity, simple interface design without complicated operation and maintenance. The TCP/IP protocol is used for data transmission over the network, and the system encrypts and decrypts a large number of user names and passwords stored in the database through a background program[10]. The application can also provide users with various forms of input and output status or other styles of menu style, and it can also be flexible to set different types of menus according to the needs of users, so as to achieve a variety of functions.

Qualitative properties of the ordinary differential equations: the present system of plane polynomials can be expressed by equation (1).

Analyze the qualitative properties of the ordinary differential equation as follows:

First, analyze the finite singularity of the ordinary differential equation: if the point VVV satisfies both equation (2), then (x', y') is the singularity of this planar polynomial system.

At this point, if the parameters a, b, c, d satisfy the equations (3) and (4), then this singularity is unique.

The qualitative form of the system can be determined by the roots of the characteristic equation of the system (characteristic roots), which is shown in Equation (5).

Equation (6) can be obtained by transforming Equation (5).

When _{1}, _{2} is the same negative real root, the corresponding singularity is a stable node; when _{1}, _{2} is the same positive real root, the corresponding singularity is an unstable node. In order to study the distribution of the trajectories over the full plane (global structure), it is also necessary to study the domain of infinitely far singularities. The parameter substitution is shown in Equation (7).

Systematizing equation (7) yields (8) as shown:

Equation (8) can be transformed into Equation (9) by a generalization.

Further parameter substitution can be done to obtain equation (10).

Simplifying equation (10) yields equation (11).

Then the infinitely far singular point on the phase plane corresponds to (11) on the z = 0 axis on the Π plane, i.e., equation (12) is obtained.

Studying the field of D, D' on the equator, then the system is substituted by the parameters to obtain the equation (13).

The simplification leads to equation (14).

The generalization leads to Equation (15).

Doing the parameter substitution yields Equation (16).

The simplification leads to equation (17).

In traditional teaching, teachers teach students to learn, but the learning efficiency is very low, but the development of modern network technology allows us to solve these problems through the computer. The mobile support system can not only improve the classroom learning effect and interactivity, but also enhance the students' mastery of the course knowledge, and reduce the teacher's teaching burden, thus increasing the students' independent participation, so that they can complete the reception of their own interest in the course in a relaxed atmosphere[11].

Ordinary differential equation is a kind of linear function, which can be created according to the need of corresponding equation, but its solution is not uniquely determined, so when we analyze the problem, we often can not get the correct answer very well. The auxiliary system can solve the equation, which requires us to design a set of software and hardware suitable for teaching needs.

1) Function fode(t,x,z): find the first order equation x= F(t,x) of the vector field function, where t,x is the independent variable and the range of values of the function, z= F(t,x) for the vector direction function, the procedure is as follows:

function w=fode(t,x,z)

[t,x]=meshgridt,x);dt=ones(size(t));

dx=eval(z);quiver(t,x,dt,dx)

The function fodeivc (z, xO, y0, x1, x2, y1, y2): find the solution of the initial value problem CCC, where x0, y0 is the initial value, x1, x2, y1, y2 is the range of values of the initial value solution, the program is as follows:

function h=fodeivc(z, xO, yO, x1, x2, y1, y2)

syms x y;

F=[’Dy=’z];

y=dsolve(F, ’y(x0)=y0’,’x’);

x=x1:0.1:x2;

y=eval(y);

plot(x,y, r);

The function todet(F,G,H,x0,y0,zO,t0,t1), whose system of equations is shown in Equation (18).

F,G,H are the right end functions of the system of equations, x0,y0,z0 are the initial values, t0,t1 are the two end points of the solution interval of the differential equation, and the procedure is as follows:

function f=todet(a,b,c,x0,y0,z0,t0,t1)

function f=todet(a,b,c,x0,y0,z0,t0,t1)

p=@(t,x)[eval(a);

eval(b);eval(c)];

u0=[x0;y0;z0];

[t,x]=ode45(p,[t0,t 1 ],u0);

figure(1);

plot(t,x);figure(2)

plot3(x(:,1),x(:,2),x(:,3));

When designing this support system, the following factors should be taken into account:

First of all, it is necessary to meet the basic needs of the user for learning tennis. The actual situation will determine what kind of model to use and how to make it. The second factor is whether the technology required for the hardware and software parts can be realized and whether the functions are perfect or not; finally, it is the rationality and scientificity of the design of the specific development process and the possible problems and solutions, so that the practical value of the auxiliary system can be truly reflected[12]. The system is designed to meet the basic functional requirements of the users for daily teaching, and it can provide users with efficient, convenient, accurate and real-time characteristics. Therefore, the overall design of the system is shown in Figure 5.

The tennis sports assistance system mainly consists of a sensing module and a cell phone APP, in which the sensing module mainly includes six-axis sensors, a microprocessor for low-power wireless communication with smart phones and a power supply module. The cell phone APP collects motion signals in real time, analyzes and displays motion results.

The sensing module is a very important component in the system design. It is not only required to provide enough complete and reliable data information for the whole system, but also requires good reliability and security to ensure the normal operation of the machine or software used in the whole project development process. Characteristic parameters (e.g., hardware environment) can be captured and saved as a reference for the next stage of work, while also taking into account the need to simplify the structure and modularity as much as possible to improve system performance during design. The structure of the sensor module is shown in Figure 7.

System development mainly includes two parts: hardware environment and software environment, of which hardware conditions are the most important part of the whole project. In this set of program design process, in order to facilitate the testing, debugging and maintenance of the modules need to choose the appropriate development tools and complete the corresponding functions; the system selected the more common and highly portable MyEclipse as the central chip to achieve development. Database as a complete architecture built up is the software platform contains and supports the entire application running requirements, it is one of the important components of the program design process. Database applications are at the core of the entire software system, a good program should not only have excellent and reliable storage and delivery of data functions, but also have a good generality of high, easy to use features.

System performance evaluation is the basis for evaluating the entire project. By testing this functional item, user requirements can be understood and the software can be improved and refined. In order to improve the system performance index: throughout the development process, it is necessary to constantly check whether the equipment used meets the user requirements. This is not only to consider the factors of the product itself, hardware conditions and other issues, but also to fully consider the degree of impact of changes in customer needs and other external environments, and also to focus on whether the product can provide better service or support to cope with the unpredictability of changes that occur in a variety of situations.

The design of a tennis auxiliary system based on ordinary differential equations is centered on user requirements, and the corresponding functional modules are created in the database for management and maintenance. According to the requirements of this system design, each component is described in detail, including auxiliary equipment, management interface and database modules.

In the system evaluation process, the development and operation efficiency of the software were mainly measured. For this auxiliary teaching aid, whether its performance meets the user's needs and whether the usage time can be satisfied will be the important criteria to evaluate the system. Therefore, it is necessary to realize the interactivity, collaboration and portability between the tennis mobile learner and traditional teaching aids through relevant technical means, and it is necessary to evaluate and analyze the problems encountered in the development process of the whole system to ensure the improvement of the software design quality; secondly, through the design of this auxiliary tool, the operation efficiency of the whole system can be improved, and it can promote the improvement of the tennis mobile teaching software to a certain extent.

At present, some universities in China have their own corresponding tennis sports assistance systems, but these functions only stay at the theoretical level and do not get enough attention, so further development is needed in the software. With the coming of the Internet era, mobile devices have become indispensable tools for people to get information, share information and communicate, and so on, and the tennis sports assistance system also comes into being. However, it is seldom applied to teaching in many universities in China, which leads to students' lack of deep understanding and mastery of the course, and the lack of teachers and hardware facilities, as well as the lack of attention to the technology in some schools, these have caused a serious lack of tennis courts and low quality, so it cannot meet the teaching needs of tennis. This paper presents a detailed analysis of the auxiliary system based on the design and implementation of the ordinary differential equation auxiliary system, which proposes and establishes a set of tennis mobile equipment management mode that is suitable for China's national conditions and can improve students' learning interest and experience effect.

Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis 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 Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules 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 Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators 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 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 Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform 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 A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project 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 An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation 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 Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation 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 Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption 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 driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country 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 Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method 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 Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation 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 Paris panxiensis , a new combination of Trilliaceae from Sichuan, ChinaImpact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method 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 Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence 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 VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ 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 -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network