After social and economic development has entered the knowledge age, human development attaches more importance to educational innovation. [1]Using the theoretical method of differential equation, the researchers conducted a preliminary study based on the mathematical model under the condition that there were only two kinds of innovation generation relations, and mainly discussed whether the explanation with the initial value far from the equilibrium point could be inclined to the equilibrium point. The differential equation model of educational innovation competition is as follows[2]:

In the above formula, K_{1} and K_{2} represent the penetration rate of educational innovation X and Y without considering the environmental impact; M_{1} and M_{2} represent the maximum possible number of X and Y; X (t) and y (t) represent the cumulative number of recipients of X and Y; B_{1} >0 and B_{2} >0 represent the interaction coefficients when X and Y coexist in the system.

According to the above formula, the positive equilibrium point
_{2}(_{1},0), _{3}(0, _{2}), is p4 (0,0). In the case of coexistence of X and Y, research and analysis can be carried out under the condition of

Suppose _{1}(^{*}, ^{*}), where
_{1} < _{2} < 1, then the following equation is satisfied:

And the above model can be transformed into:

The corresponding function formula is:

The final calculation is as follows:

It follows that V (x, y) is a positive definite function inside R2, and as it approaches the x or y axis, it satisfies the condition

Thus, it can be obtained:

At the same time, because X axis and Y axis belong to the internal track of the system, there will be no closed track outside the three equilibrium points p2 (M1, 0), P3 (0, M2) and P4 (0, 0), otherwise there will be conflicts with the intersection of X axis and Y axis.

Under the condition that B1B2 =1, there is a balance between the axial line L1:

Under the condition of _{1}_{2} ≠ 1, limit cycles will not appear outside the equilibrium point

Assuming
^{α}^{−1}^{β}^{−1} is obtained inside the first quadrant, where

Since the corresponding symbols of X and y have been identified in the study, the following requirements should be met in order to ensure the invariable sign of D:

From this, it can be calculated:

And:

Assuming constant _{1}(_{1}−1)+_{2} (_{2}−1) ≠ 0 meets this condition, it is proved that the system does not have closed orbits. If the constant _{1} (_{1} −1)+ _{2} (_{2} −1) = 0 satisfies this condition, then the proof system also has no limit cycles.

Researchers proposed a complementary differential equation model of educational innovation with the Logistic equation as the core, as shown below[3]:

In the above model, the positive equilibrium point

The equilibrium point of the above model is
_{2} (_{1},0), _{3} (0, _{2}) p4 (0,0). In the case of coexistence of X and Y, research and analysis can be carried out under the condition of

Suppose _{1}(_{1}, _{2} < 1, then the following equation is satisfied:

Convert the above formula to:

And get:

The actual calculation results are:

So V of x, y is a positive definite function inside R2, and as (x, y) approaches the x and y axes, we get

The total derivative of V (x, y) according to the above model is:

Under the condition of _{1}_{2} ≠ 1, limit cycles will not appear outside the equilibrium point

^{α−1} ^{β−1}, where

After the symbols of x and y are specified, in order to keep D unchanged, the following requirements must be met:

It can be calculated as follows:

And:

Assuming constant _{1}(_{1} −1)+ _{2} (_{2} −1) ≠ 0 meets this condition, combined with the above studies, it is proved that the system does not have closed orbits.

To put it simply, the evaluation of network education comprehensive management efficiency is to study the relationship between output and input during teaching management, so as to better understand the ability of network education in colleges and universities to allocate resources, as well as the sustainable development and competition level in the market competition. Starting from different research perspectives, the efficiency of online education in colleges and universities can be divided into two situations, one is technical efficiency, the other is scale efficiency, the former refers to the highest output level of online education under given input conditions, while the latter refers to whether online education can be operated under standard investment. According to the analysis of the single input and single output efficiency curve shown in FIG. 1 below, the production function y=f (x) represents the maximum output y that can be obtained when the production is in the optimal state.[4]

The technical efficiency studied in this paper mainly analyzes the distance between network education teaching and production function. Assuming that the teaching center of A university operates at point A, the actual technical efficiency can be calculated as follows:

Technical efficiency of A = Bd/bA

Because the production function represents the relationship between input and output under the ideal state, all teaching centers in colleges and universities will operate below the production function curve, with the technical efficiency ≤1. The technical efficiency of online education on the production function curve =1, also known as technical efficiency.

Point E divides the production function into two parts. The function on the left keeps rising, which means that increasing the amount of input can increase output, and online education has the initiative of investment. This range can be regarded as the stage of increasing returns to scale. Glaze function is in a continuous decline stage. In the case that the investment amount is X, if it continues to increase, the efficiency of output improvement is not high. At this time, online education has no enthusiasm to continue investment. It can be seen that the input scale represented by point E is the most appropriate. Generally speaking, the calculation formula of scale efficiency of online education in colleges and universities is as follows: The scale efficiency of A is equal to B C over B D

In general, scale efficiency ≤1 is regarded as scale effective when it is equal to 1. The online education represented by point E is scale effective, while the online education represented by A, D and F is not effective.

At present, online education in Colleges and universities in China has begun to cultivate talents needed for national construction in large quantities. This study selected the education center of online education college built in a certain place for empirical analysis, including 13 teaching centers as the evaluation target, and evaluated their output orientation and management effectiveness. The specific results are shown as follows[5]:

First, data sets. The index data of the teaching center in 2020 are selected to form the input-output data set, as shown in Table 1 below:

Input-output data sets of online education institutes in different regions

The teaching center The evaluation index | Input indicators | Output indicators | |||||
---|---|---|---|---|---|---|---|

The average number of (X1) | Number of receiving devices (X2) | Number of multimedia classrooms (X3) | Number of networked computers (X4) | Number of students graduating in the year (Y1) | Employment rate (Y2) | Average Grade (Y3) | |

Tianjin First Teaching Center | 41 | 5 | 5 | 150 | 54 | 32.3 | 78 |

Tianjin Second Teaching Center | 71 | 1 | 7 | 180 | 247 | 20.5 | 76 |

Tianjin Third Teaching Center | 44 | 1 | 6 | 40 | 75 | 60.8 | 72 |

Tianjin Fourth Teaching Center | 90 | 2 | 5 | 150 | 243 | 33.4 | 79 |

Tianjin Fifth Teaching Center | 55 | 1 | 5 | 248 | 102 | 46.2 | 78 |

Tianjin Sixth Teaching Center | 19 | 1 | 3 | 80 | 86 | 50.6 | 75 |

Tanggu Teaching Center | 34.5 | 1 | 9 | 250 | 270 | 61.8 | 85 |

Dagang branch | 9.5 | 1 | 2 | 40 | 117 | 42 | 72 |

Tertiary Teaching Center | 59 | 1 | 10 | 85 | 356 | 68.9 | 73 |

Shenzhen Teaching Center | 39.5 | 1 | 15 | 300 | 146 | 76.2 | 82 |

Jinzhou Teaching Center | 51 | 1 | 4 | 200 | 107 | 80 | 66 |

Huludao Teaching Center | 33 | 2 | 11 | 150 | 301 | 83.6 | 54 |

Zhengzhou Teaching Center | 42 | 1 | 1 | 60 | 43 | 75 | 69 |

Second, evaluate the results. Based on the linear gauge construction of the above education centers, the corresponding efficiency values can be calculated, as shown in Table 2 below:

Efficiency evaluation results of online education institutes in different regions

Tianjin First Teaching Center | Efficiency value (^{3} |
---|---|

Tianjin Second Teaching Center | 0.40 |

Tianjin Third Teaching Center | 0.99 |

Tianjin Fourth Teaching Center | 1.00 |

Tianjin Fifth Teaching Center | 0.92 |

Tianjin Sixth Teaching Center | 1.00 |

Tanggu Teaching Center | 1.00 |

Dagang branch | 1.00 |

Tertiary Teaching Center | 1.00 |

Shenzhen Teaching Center | 1.00 |

Jinzhou Teaching Center | 1.00 |

Huludao Teaching Center | 1.00 |

Zhengzhou Teaching Center | 0.97 |

Tianjin First Teaching Center | 1.00 |

Third, result analysis. Efficiency is 1 of the teaching center's comprehensive management efficiency has effectiveness. Combined with the results obtained from the above research, it is proved that the teaching center with efficiency, quality and effectiveness has cultivated a large number of graduates with a higher actual employment rate, although it has invested less manpower and equipment. However, other teaching centers with relatively ineffective management efficiency need to be further promoted and eradicated, only in this way can the management efficiency be guaranteed to be effective.

Fourthly, study on evaluation of super efficiency. Combined with the above research results, the Education Center of College of Network Education is selected as the DMU and its indicators in 2020 are selected, as shown in Table 3 below:

Evaluation results of central efficiency of online education colleges in different regions

Tianjin First Teaching Center | Efficiency value (^{3} |
Super efficiency value (SE-DEA) |
---|---|---|

Tianjin Second Teaching Center | 0.40 | 0.40 |

Tianjin Third Teaching Center | 0.99 | 0.99 |

Tianjin Fourth Teaching Center | 1.00 | 1.00 |

Tianjin Fifth Teaching Center | 0.92 | 0.92 |

Tianjin Sixth Teaching Center | 1.00 | 1.00 |

Tanggu Teaching Center | 1.00 | 1.02 |

Dagang branch | 1.00 | 1.16 |

Tertiary Teaching Center | 1.00 | 2.21 |

Shenzhen Teaching Center | 1.00 | 2.33 |

Jinzhou Teaching Center | 1.00 | 1.09 |

Huludao Teaching Center | 1.00 | 1.08 |

Zhengzhou Teaching Center | 0.97 | 0.97 |

Tianjin First Teaching Center | 1.00 | 3.57 |

According to the above numerical calculation and analysis, the final super-efficiency evaluation results prove that the management effectiveness of online education is higher if the value is greater than or equal to 1. Research integrated management effectiveness of university network education, compared with traditional assessment methods, this paper studies on the basis of the construction of ordinary differential equation model for the empirical analysis, is on the basis of the related numerical carried on deep discussion, finally it is concluded that the evaluation results more objective and fair, to an invalid network education put forward effective improvement scheme, And provide scientific basis for educational administrators to make relevant policies[6].

In recent years, China's university network education has begun to take shape, especially after the construction of modern distance education cooperation group, gradually expand the scope and level of university network education institutions of cooperation. For example, in the development of curriculum resources, based on cooperative discussion to master more educational courseware; In the construction of learning sites and face-to-face guidance, the construction of resource sharing platform. However, nowadays network education in colleges and universities is still promoting relatively independent teaching plans and management strategies, so it is difficult to build a good cooperation platform. Therefore, on the basis of clarifying the importance of cooperation among colleges and universities, the educational administrative departments should construct the cooperation platform of network education according to the educational nature of colleges and universities in different regions, and clarify the standardized courses and educational services shared by colleges and universities. In the case of mature conditions, we can also draw lessons from western virtual universities, develop similar educational programs and teaching courses, and uniformly issue academic degrees, so as to show the advantages of network education of colleges and universities in different regions.[7]

Network technology makes university education work more interesting, the actual education resources more abundant, the teaching content more vivid and dynamic, can carry out all-round and diversified teaching guidance to accept educators. According to the characteristics analysis of online education as shown in the figure below, current investigations and studies show that when humans receive external information, 30% of them rely on vision, 11% on hearing, 1% on taste, 1.5% on touch and 3.5% on smell. Therefore, multi-channel transmission of educational knowledge is more effective than single channel. Network education in colleges and universities to help students to obtain access to information from various angles, there are a lot of common channel, for instance in network channels to collect readings, download the music platform audio clip, in a web page to watch 2 d or 3 d images, etc., can participate in teaching activities, fully mobilize students' various senses and can focus on the students' attention, Enable them to master the knowledge in accelerated comprehension and full expression.[8]

In the design and promotion of institutions, network education belongs to the basic content of educational management in colleges and universities. Based on the analysis of the requirements put forward by the current education department, it contains the organizational structure and responsibilities and functions as shown in the following table. Although the overall design of institutions and departments is very perfect, the communication and cooperation between various departments should be strengthened in the development of practice. Only in this way can the management level of practice education be improved and the cultivation of professional talents be done well.

Organizational structure, responsibilities and functions of online education in colleges and universities

Set up agencies | Organizational functions and responsibilities |
---|---|

Administration department | Responsible for the daily affairs and management of the Network College; Responsible for the personnel management of the Network College; Responsible for the coordination of various departments and rooms within the college, the external liaison work of the network college and the internal financial management of the college. |

Academic affairs department | Responsible for the recruitment of network college; Responsible for the development of various types of education programs, the development of teaching plans, teaching programs; Organize and hire teachers to implement network teaching, including teaching, online tutoring and answering questions, homework correction, experiment and practice teaching, graduation defense, etc., the development of network courses and various teaching course assessment, credit recognition, certificate issuance; Student course selection management. |

Technical department | Responsible for the construction and management of off-campus teaching stations; Network college all teaching equipment management and maintenance; Research and development of network teaching platform; Network college website construction and maintenance, update and daily management. |

In the network education of colleges and universities, the continuous optimization of teachers' educational ideas and the enrichment of teachers' source channels are conducive to the rational allocation of teachers' resources while sharing them. First of all, diversity of teachers should be guaranteed. As more of a college network education to guide teachers in the social, so colleges can directly to the social demand positioned and open recruitment, so don't need to worry about the teacher's geographical location, no longer depend on the unified textbooks, but on the basis of widely collecting network data access to the most practical and most innovative knowledge technology. Secondly, the intellectual resources of teachers should be integrated. The lack of sufficient teachers is a major obstacle to the implementation of higher education in China, and online education has no limitations in age and other aspects. As long as individuals can meet the needs of online education, they can find suitable positions. It can not only change the collective behavior of teachers, but also optimize the organizational form and professional division of the existing network education by allowing outstanding talents from all fields of society to participate in the network education work, comprehensively integrating the governance resources of the society and enhancing the cooperative and interactive relationship between education. Finally, it is helpful for professional teachers to participate in scientific research and ability training. The large-scale promotion of network education in colleges and universities has put forward higher requirements for professional teachers. On the one hand, they need to expand their horizons, update their knowledge structure and technical ability in time, and quickly grasp the core achievements of the new direction of modern science and technology development. On the other hand, according to the changing trend of the growth of human science and technology knowledge, we should integrate the most advanced and novel knowledge and technology into the teaching work, keep the enthusiasm of learning and discussion for a long time, pay attention to the construction and promotion of knowledge system, so as to improve our comprehensive education management level.[9, 10, 11]

To sum up, in the steady development of online education in Colleges and universities in China, the implementation quality and management efficiency are the main direction of empirical research. At present, theoretical analysis and empirical research on network education in colleges and universities are in the stage of development to be improved, and there are many problems that have not been solved. Therefore, researchers and scholars should enrich the research results in this field in continuous exploration and pay attention to the rational use of ordinary differential equation model for review and research. Only in this way can network education in colleges and universities become the main direction of educational innovation in the future and truly meet the increasing personalized learning needs of the masses of citizens.

#### Efficiency evaluation results of online education institutes in different regions

Tianjin First Teaching Center | Efficiency value (^{3} |
---|---|

Tianjin Second Teaching Center | 0.40 |

Tianjin Third Teaching Center | 0.99 |

Tianjin Fourth Teaching Center | 1.00 |

Tianjin Fifth Teaching Center | 0.92 |

Tianjin Sixth Teaching Center | 1.00 |

Tanggu Teaching Center | 1.00 |

Dagang branch | 1.00 |

Tertiary Teaching Center | 1.00 |

Shenzhen Teaching Center | 1.00 |

Jinzhou Teaching Center | 1.00 |

Huludao Teaching Center | 1.00 |

Zhengzhou Teaching Center | 0.97 |

Tianjin First Teaching Center | 1.00 |

#### Evaluation results of central efficiency of online education colleges in different regions

Tianjin First Teaching Center | Efficiency value (^{3} |
Super efficiency value (SE-DEA) |
---|---|---|

Tianjin Second Teaching Center | 0.40 | 0.40 |

Tianjin Third Teaching Center | 0.99 | 0.99 |

Tianjin Fourth Teaching Center | 1.00 | 1.00 |

Tianjin Fifth Teaching Center | 0.92 | 0.92 |

Tianjin Sixth Teaching Center | 1.00 | 1.00 |

Tanggu Teaching Center | 1.00 | 1.02 |

Dagang branch | 1.00 | 1.16 |

Tertiary Teaching Center | 1.00 | 2.21 |

Shenzhen Teaching Center | 1.00 | 2.33 |

Jinzhou Teaching Center | 1.00 | 1.09 |

Huludao Teaching Center | 1.00 | 1.08 |

Zhengzhou Teaching Center | 0.97 | 0.97 |

Tianjin First Teaching Center | 1.00 | 3.57 |

#### Input-output data sets of online education institutes in different regions

The teaching center The evaluation index | Input indicators | Output indicators | |||||
---|---|---|---|---|---|---|---|

The average number of (X1) | Number of receiving devices (X2) | Number of multimedia classrooms (X3) | Number of networked computers (X4) | Number of students graduating in the year (Y1) | Employment rate (Y2) | Average Grade (Y3) | |

Tianjin First Teaching Center | 41 | 5 | 5 | 150 | 54 | 32.3 | 78 |

Tianjin Second Teaching Center | 71 | 1 | 7 | 180 | 247 | 20.5 | 76 |

Tianjin Third Teaching Center | 44 | 1 | 6 | 40 | 75 | 60.8 | 72 |

Tianjin Fourth Teaching Center | 90 | 2 | 5 | 150 | 243 | 33.4 | 79 |

Tianjin Fifth Teaching Center | 55 | 1 | 5 | 248 | 102 | 46.2 | 78 |

Tianjin Sixth Teaching Center | 19 | 1 | 3 | 80 | 86 | 50.6 | 75 |

Tanggu Teaching Center | 34.5 | 1 | 9 | 250 | 270 | 61.8 | 85 |

Dagang branch | 9.5 | 1 | 2 | 40 | 117 | 42 | 72 |

Tertiary Teaching Center | 59 | 1 | 10 | 85 | 356 | 68.9 | 73 |

Shenzhen Teaching Center | 39.5 | 1 | 15 | 300 | 146 | 76.2 | 82 |

Jinzhou Teaching Center | 51 | 1 | 4 | 200 | 107 | 80 | 66 |

Huludao Teaching Center | 33 | 2 | 11 | 150 | 301 | 83.6 | 54 |

Zhengzhou Teaching Center | 42 | 1 | 1 | 60 | 43 | 75 | 69 |

#### Organizational structure, responsibilities and functions of online education in colleges and universities

Set up agencies | Organizational functions and responsibilities |
---|---|

Administration department | Responsible for the daily affairs and management of the Network College; Responsible for the personnel management of the Network College; Responsible for the coordination of various departments and rooms within the college, the external liaison work of the network college and the internal financial management of the college. |

Academic affairs department | Responsible for the recruitment of network college; Responsible for the development of various types of education programs, the development of teaching plans, teaching programs; Organize and hire teachers to implement network teaching, including teaching, online tutoring and answering questions, homework correction, experiment and practice teaching, graduation defense, etc., the development of network courses and various teaching course assessment, credit recognition, certificate issuance; Student course selection management. |

Technical department | Responsible for the construction and management of off-campus teaching stations; Network college all teaching equipment management and maintenance; Research and development of network teaching platform; Network college website construction and maintenance, update and daily management. |

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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 Application of improved RBF neural network algorithm in hierarchical management of enterprise 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