Many factors influence exercise persistence. But broadly speaking, the theory can be grouped into two categories: personal factors and environmental factors. Humans are active creatures, and they do not respond mechanically to external environmental stimuli. The social cognitive theory also points out that individuals have self-rationality. They can generate purposeful behavior to achieve a set goal actively. Individual behavior is neither a passive response to environmental stimuli nor a mechanized judgment and loop on a feedback loop . Individual behavior results from the interaction between the environment, cognition, and behavior, which is the core of the individual's cognitive ability. The intervention of cognition makes the cognition of individual behavior different from both animals and machines. It is manifested as an organism with self-management ability, real-time dynamic change, and an active regulation system. Self-management is a series of behaviors by individuals actively setting goals, taking actions, monitoring and evaluating their performance, and making corresponding adjustments. These behaviors help individuals shape the process of their destiny . This study believes that physical exercise behavior is a kind of physical activity carried out by individuals voluntarily. This action highlights the initiative and self-control of exercise, and the exerciser is the main body and has the leading role. Individuals are very autonomous when performing physical exercise. Physical activity can actively coordinate individual and environmental factors. Self-management of exercise behavior is to use metacognition and social and material environment to set exercise goals and choose exercise content and methods under the guidance of exercise motivation. They achieve the exercise goals by self-monitoring the exercise process and evaluating the exercise results promptly. If college students improve their exercise behavior, they must improve their self-discipline and self-management level. Self-management has powerful applications for improving performance. At the same time, performance has a feedback effect on individual behavior. The quality of performance is an important basis for adjusting behavior. Good exercise effect can promote exercise persistence is the first hypothesis of this study. The level of self-management affects the completion of people's work and study tasks . This indicator ultimately affects the persistence of individual exercise behavior. Therefore, the research on exercise behavior must emphasize the self-management ability of exercisers. This is the certainty of the mutual unity of external and internal causes, other masters, and autonomy.
Some studies have found a significant correlation between exercise motivation and exercise persistence. Exercise atmosphere is also an important factor affecting exercise persistence. If you want to improve the exercise behavior of college students, college students must improve their self-discipline and self-management level. Therefore, we believe that exercise motivation and exercise atmosphere have predictive effects on exercise persistence. Self-management of physical exercise behavior is that individuals actively adjust the external exercise environment, internal exercise motivation, and other factors. And this principle has an impact on exercise persistence . This satisfies the criterion for the mediation effect. Therefore, Hypothesis 2 is that self-management of physical exercise behavior plays a mediating role between exercise motivation, exercise atmosphere, and persistence. In addition, studies have shown that physical exercise behavior has age and gender differences. Therefore, whether there are age and gender differences in the self-management model of physical exercise behavior is another question to be studied in this study. This also becomes hypothesis 3 of this study.
The term “central limit theorem” was introduced by Polya in 1920. The central limit theorem is a class of theorems in probability theory that study the sequence parts and distributions of random variables. The theorem asserts that the probability distribution of the sum of a large number of independent random variables approximates the normal distribution under appropriate conditions. It is an important part of probability theory and one of the cornerstones of mathematical statistics . For two centuries, the limit theorem was a central research topic in probability theory. At present, few thinkers of the limit theorem in the system research center at home and abroad, especially the introduction to the probability thought of the St. Petersburg School of Probability Theory, can only be found in the general history of mathematics works. No scholar has yet combined probability theory with the academic theory of sports. This is undoubtedly a pity. Therefore, this paper studies the relationship between college students' physical exercise motivation and self-control ability by using the mathematical model of probability theory. We use probabilistic path analysis to test the fit and difference of the relationship between the two. To explore the effect of physical exercise behavior self-management on exercise atmosphere, exercise motivation, and exercise persistence.
We used a stratified random sampling method. At the same time, we sampled by grade at 3 universities. A total of 600 college students were tested in groups in this experiment. The scale was filled out on the spot and returned. Five hundred sixty-three valid questionnaires were recovered (170, 152, 160, and 81 from freshman to senior year, respectively . The ratio of males and females in each grade was equal: 320 males and 243 females). The effective recovery rate was 93.8%.
The Physical Exercise Motivation Scale for College Students contains 4 subscales. The content includes self-breakthrough, ability, independent choice, and personal input. A total of 16 projects. We use a 5-point Likert scale. The scoring is indicated from “1” (none at all) to “5” (very strong). The internal consistency reliability of the measurements was 0.79.
“College Students' Physical Exercise Atmosphere Scale” is adapted from the Youth Outdoor Sports Atmosphere Scale . A total of 5 subscales. The content includes 17 interpersonal associations, natural associations, information acquisition, interpersonal barriers, and conditional barriers. We use a 5-point Likert scale. The scoring is indicated from “1” (none at all) to “5” (very strong). The internal consistency reliability of the measurements was 0.81.
The Physical Exercise Persistence Scale for College Students was adapted from the Outdoor Sports Persistence Scale for Teenagers. A total of 6 projects. We use a 5-point Likert scale. The scoring is indicated from “1” (none at all) to “5” (very strong). The internal consistency reliability of the measurements was 0.78.
We selected 81 students from two classes in the first year of colleges and universities. We performed test-retest reliability tests at 3-week intervals. The test-retest reliability was 0.78, 0.71, and 0.75, respectively. A total of 5 experts (4 professors of physical education and 1 professor of psychology) were invited to evaluate the validity of the questionnaire. The effective rates were 82%, 86%, and 90%, respectively.
The “College Student Physical Exercise Behavior Self-Management Scale” contains 4 subscales. The content includes method management, time management, content management, and motivation management. A total of 19 projects. We use a 5-point Likert scale. The scoring is indicated from “1” (completely disagree) to “5” (completely agree). The internal consistency reliability of the measurements was 0.71.
This study used SPSS13.0 and AMOS7.0 statistical software to analyze the data. Results are expressed as (mean ± standard deviation). Mathematical test P<0.01 was considered to be very significant.
We use the generating function to prove the central limit theorem of probability theory. Laplace introduced the generating function in the 19th century. It was the first systematically applied transformation method in probability theory. This method is useful for integer-valued random variables . This theory is the precursor to the characteristic function. The Z-transform method developed has become an important method to solve many problems. The most basic property of the generating function is that the generating function of the sum of independent random variables is equal to the product of the original generating function. This brings convenience to the calculation. Chebyshev gave the following proof:
We assume that the probability of random variable
We assume that
Using the properties of the generating function, we get
Since B is the sum of variances, positive numbers increase as the number of random variables increases. Chebyshev assumes that the upper limit of the integral is infinite, then we have
Then we get the integral theorem
Chebyshev used the method of moments to solve many difficult limit estimation problems. We apply it to the proof of the Central Limit Theorem. We use
Markov made an in-depth study of Chebyshev's moment problem. In the article, he extended the Chebyshev problem as follows:
(2) 0 ≤ (3)
(2) 0 ≤
Here comes the rudiment of the functional. Markov solved the problem under the condition that the
Dutch mathematician Stergis also conducted similar research at the same time. He gave results similar to Markov's. This theory solves the moment problem on the infinite interval (0, ∞). They give continuous fraction expressions for all integer moments of the function they are looking for. Markov's “Two Proofs of Convergence of Certain Continued Fractions,” published in 1895, gave the necessary and sufficient conditions for achieving Sgyersian continued fractions.
Chebyshev used the method of moments to prove the Central Limit Theorem. Suppose the random variable sequence any For any
Markov proved some of the inequalities given by Chebyshev in 1884. This undoubtedly accelerated Chebyshev's research. In 1886 Chebyshev proved that if If (1) (2) Suppose
Mean, standard deviation, and difference comparison of scores for each test variable
|Primary level||Senior grades||F|
Pearson correlation analysis for each variable
|1) Exercise atmosphere||-|
|2) Exercise motivation||0.514||-|
|4) Method management||0.485||0.688||0.855||-|
|5) Time management||0.368||0.564||0.816||0.656||-|
|6) Content management||0.426||0.658||0.664||0.646||0.468||-|
There are significant gender differences in the three indicators of exercise atmosphere, motivation, and adherence in college students' self-management of exercise behavior (P<0.01). Boys scored significantly higher than girls. This study classified first- and second-year students as lower grades . The third and fourth grades are classified as the senior group. The scores of method management, content management, motivation management, exercise motivation, and exercise adherence in the self-management of the lower grades were higher than those of the upper grades. The data were very significant (P<0.01). Self-management and its four dimensions were significantly correlated with exercise atmosphere, motivation, and persistence (P<0.01).
This study constructed a mediating model of exercise behavior self-management between exercise motivation, exercise atmosphere, and persistence. Among them, exercise behavior self-management is the mediating variable of exercise motivation and exercise atmosphere on exercise persistence. We use AMOS7.0 for path analysis. The initial model contains all the path relationships between the independent and dependent variables. The analysis results showed that the direct path coefficients from exercise atmosphere to persistence were not significant . According to this result, we delete the insignificant paths and analyze the fitting degree of the data. The results show that the modified comprehensive cognitive model has a better fitting degree. The path coefficients of each model are shown in Figure 1. The model fit index is as follows:
The results show that the model fits well. The relationship between the training atmosphere and the persistence of exercise is carried out through the full mediating effect of self-management. However, self-management in the relationship between exercise motivation and persistence is only a partial mediator. It increases the direct effect of exercise motivation on persistence. In addition, the effect of exercise motivation on self-management of exercise behavior is greater than that of exercise atmosphere on self-management of exercise behavior . All path coefficients of the modified model are significant. The fit of the whole model reached a high standard of fit. The hypothetical model proposed in this study fits well with the observed data. The external quality of the model is good.
The purpose of multi-group structural equation model analysis is to explore whether the path model diagram suitable for a certain group is also suitable for other groups. The article evaluates whether the hypothetical model proposed by the researcher is equal or the parameters are invariant among different samples. In this study, the fitting test of the multi-group structural equation model was carried out using different demographic characteristics of college students and the exercise behavior self-management hypothesis model. This explores how the variables in the hypothetical model behave in different groups.
We used multi-group comparisons to test gender and grade differences in the revised exercise behavior self-management model . The path coefficients corresponding to the two groups of the different group-defining structural model parts are equal. Table 3 lists the path coefficients of the exercise behavior self-management models for different gender and grade groups. By comparing the critical values of the differences between model parameters, it is found that there are significant differences in the paths of exercise motivation pointing to self-management and exercise motivation pointing to persistence. The critical ratios on these two pathways were −2.131 and 2.040 for men and women, respectively. These values were all greater than 1.96 (P<0.05). The other path coefficients are less than 1.96, and the difference is insignificant (P>0.05). There was no significant difference in path coefficients (P>0.05). This indicates that gender has a significant moderating effect on the self-management model of college students' exercise behavior, but grade has no moderating effect. In the influence of exercise motivation on self-management, the path coefficient of boys is significantly higher than that of girls. In the influence of exercise motivation on persistence, the path coefficient of girls is significantly higher than that of boys.
Comparison of critical ratios of standardized path coefficients for each group model by grade and gender
|Boy||Girl||Critical ratio||Difference test (P value)|
|Primary level||Senior grades||Critical ratio||Difference test (P value)|
There are significant gender differences in the three indicators of exercise atmosphere, motivation, and adherence in college students' self-management of exercise behavior (P<0.01). Boys scored significantly higher than girls. Most existing studies have found significant differences between boys and girls in their motivation to exercise. Boys tend to be more intense, aggressive big ball games and small ball games that reflect personal skills. Girls are more likely to choose sports with a small amount of exercise or a body sculpting effect. However, research shows that most students hope to improve their physical fitness through physical exercise to adapt to the competitive social environment in the future. This intrinsic motivation is long-term and persistent. This is unshakable in the subjective consciousness. This is also the ultimate goal for male and female college students to exercise motivation management. Therefore, gender differences in motivation management were not significant. This is consistent with the results of this study. Social and cultural influences on gender shaping and biological differences. Most boys have stronger athletic abilities and hobbies than girls. As a result, boys have stronger self-management skills than girls.
There are gender differences between boys and girls informing exercise habits and persisting in physical exercise. Boys exercise longer than girls. Because social role positioning endows men with robustness and liveliness. Women tend to be slender and quiet. Therefore, boys are more able to participate and persist in exercising. The scores of method management, content management, and motivation management in the self-management of the lower grades are higher than those of the upper grades. This may be due to the introduction of physical education classes in the first and second years of college. Students scored higher than their seniors in third and fourth grades who did not have physical education in all aspects of method management, content management, and motivation management. Because of the physical exam, the lower grades are also more motivated to exercise than the upper grades. College students of all grades have relatively little time to participate in physical exercise objectively due to their wide range of hobbies and learning tasks. Some college students do have certain deficiencies in time management. Therefore, the grade difference in time management was not significant. The exercise atmosphere can play an exemplary role, a driving role, a motivating role, and an educational role. Still, people can only identify the exercise group by gender rather than grade. Therefore, exercise climate affects gender regardless of grade.
In this study, exercise climate and exercise motivation were used as independent variables, and persistence was used as the dependent variable to test the mediating effect of exercise behavior self-management in the two. The fit analysis of college students' exercise behavior self-management model shows that the revised model fits better. Physical exercise motivation refers to the psychological motivation of people to participate in and maintain physical exercise behavior, and it is the direct cause of physical exercise behavior. The exercise atmosphere can play an exemplary role, a driving role, a motivating role, and an educational role. This is an important factor affecting the formation of physical exercise habits of middle school students. After confirming the relationship between exercise climate and exercise motivation and persistence, it is particularly important to explore how self-management affects persistence. We must explore the mechanism of self-management affecting persistence to analyze the psychological mechanism of the relationship between the two. Some scholars have pointed out two modes in which individual behavior can be changed: one is external influence. This is a model managed by others. The other is the mode of individual self-management. The individual himself is always the “protagonist” of the entire process of behavior change, and the actor himself participates in the process of making plans, specifying goals, arranging the environment, implementing operations, and evaluating effects in the process of behavior change.
Individuals need to use various cognitive and behavioral strategies to regulate their thoughts, emotions, behaviors, and the environment in which they live to achieve set goals. This is the individual self-rationality pointed out by social cognitive theory. This indicates the mediating effect of self-management among exercise climate, exercise motivation, and persistence. The mediating variables are the intrinsic and substantive reasons exercise climate and exercise motivation affect exercise persistence. Exercise behavior self-management plays a mediating role in the relationship between college students' exercise atmosphere, motivation, and persistence. This validates Hypothesis 2 of this study. At the same time, this also proves the effect of exercise behavior self-management on exercise persistence. Our conclusion makes Hypothesis 1 also verified.
The relationship between exercise atmosphere and exercise persistence in the self-management model of college students' exercise behavior is carried out through the full mediating effect of self-management. Self-management is only a partial mediator in the relationship between exercise motivation and persistence. The content contains the direct effect of exercise motivation on persistence. In addition, the mediating effect of exercise self-management between exercise motivation and persistence is larger than that between exercise atmosphere and persistence. Students can consciously regulate and control their thoughts, motivations, and behaviors. And the effect of exercise behavior on exercise motivation is stronger. Because motivation is an internal controllable factor, and the environment (atmosphere) is an external, uncontrollable factor. Therefore, the individual's subjective initiative for motivation is stronger than the effect on the atmosphere. This shows that college students' exercise motivation is very important to their exercise persistence. It has an irreplaceable role in self-management.
Gender has a significant moderating effect on college students' exercise behavior self-management model, but grade has no moderating effect. This part verifies Hypothesis 3 of this study. Specifically, in the influence of exercise motivation on self-management, the path coefficient of boys is significantly higher than that of girls. In the influence of exercise motivation on persistence, the path coefficient of girls is significantly higher than that of boys. Boys have stronger self-management skills than girls. Boys are also more motivated to exercise than girls. In addition, motivation is an inherently controllable factor. Environment (atmosphere) is an external and uncontrollable factor. The individual's subjective initiative for motivation is stronger than the effect on the atmosphere. Therefore, in the influence of exercise motivation on self-management, the path coefficient of boys is significantly higher than that of girls. The appearance motivation of female college students is stronger than that of boys, which is in line with the psychological characteristics of contemporary women's pursuit of physical beauty. Appearance motivation belongs to internal motivation and is more conducive to exercise behavior. Therefore, girls' strong demand for physical beauty will generate positive exercise motivation and directly affect exercise behavior. Girls' exercise motivation has a stronger direct effect on persistence than boys.
This study investigated the model of college students' exercise behavior persistence from self-management. The conclusions of this study enrich the theory of exercise psychology. This provides a scientific basis for implementing the study of exercise persistence among college students. The college stage is a critical period for developing lifelong sports. Good exercise behavior self-management ability will effectively ensure exercise persistence. The conclusions drawn from the article can promote lifelong sports in adolescents. This study provides preliminary support for gender and grade differences in the mediating effect of exercise behavior self-management.
Comparison of critical ratios of standardized path coefficients for each group model by grade and gender
|Boy||Girl||Critical ratio||Difference test (P value)|
Mean, standard deviation, and difference comparison of scores for each test variable
Pearson correlation analysis for each variable
|1) Exercise atmosphere||-|
|2) Exercise motivation||0.514||-|
|4) Method management||0.485||0.688||0.855||-|
|5) Time management||0.368||0.564||0.816||0.656||-|
|6) Content management||0.426||0.658||0.664||0.646||0.468||-|
|8) Persistence||0.462||0.660||0.668||0.628||0.466||0.628||0.408||-|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 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 Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk 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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 A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes 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 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 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 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 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 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 of p-groups The 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 Research on threat assessment problems of island air defence system based on the leader-follower model 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 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 Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H2-N2 atmosphere Algorithm 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 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model