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 [1]. 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 [2]. 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 [3]. 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 [4]. 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 [5]. 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 [6]. 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 [7]. 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 [8]. 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 _{i}_{i}_{i}_{i}_{i}_{i}

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:

Known (1)

(2) 0 ≤

(3)

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 _{1}, _{2} … _{n}_{k}_{k}

any _{k}_{k}

For any _{k}_{k}_{ξn}

Markov proved some of the inequalities given by Chebyshev in 1884. This undoubtedly accelerated Chebyshev's research. In 1886 Chebyshev proved that if _{k}_{k}

If (1) _{1}, _{2} … _{n}

(2) Suppose

The mean, standard deviation, and Pearson correlation coefficient of each variable are shown in Table 1 and Table 2.

Mean, standard deviation, and difference comparison of scores for each test variable

Test variable | Gender | ||
---|---|---|---|

Male | Female | F | |

Exercise atmosphere | 55.51±6.91 | 51.45±7.65 | 0.27 |

Exercise motivation | 51.26±9.95 | 44.79±10.82 | 1.71 |

Self-management | 65.87±12.57 | 61.15±12.04 | 0.08 |

Method management | 10.22±6.45 | 27.41±6.55 | 0.09 |

Time management | 12.81±1.14 | 11.92±1.21 | 0.06 |

Content management | 10.92±2.57 | 9.98±2.58 | 0.51 |

Motivation management | 11.90±2.19 | 11.81±2.16 | 0.51 |

Persistence | 20.88±4.62 | 16.89±5.62 | 6.44 |

Test variable | Grade | ||
---|---|---|---|

Primary level | Senior grades | F | |

Exercise atmosphere | 54.61±7.19 | 51.11±7.61 | 0.81 |

Exercise motivation | 48.91±10.92 | 41.87±11.58 | 1.42 |

Self-management | 61.91±12.11 | 59.81±12.17 | 0.61 |

Method management | 28.95±6.48 | 26.88±6.71 | 0.61 |

Time management | 12.11±1.18 | 11.91±1.28 | 0.77 |

Content management | 10.55±2.61 | 9.61±2.55 | 0.02 |

Motivation management | 12.09±2.19 | 11.16±2.25 | 0.54 |

Persistence | 19.25±5.19 | 15.82±5.81 | 4.78 |

Pearson correlation analysis for each variable

Test variable | 1) | 2) | 3) | 4) | 5) | 6) | 7) | 8) |
---|---|---|---|---|---|---|---|---|

1) Exercise atmosphere | - | |||||||

2) Exercise motivation | 0.514 | - | ||||||

3) Self-management | 0.512 | 0.635 | - | |||||

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 | - | ||

7)Motivation management | 0.316 | 0.421 | 0.614 | 0.468 | 0.266 | 0.516 | - | |

8) Persistence | 0.462 | 0.660 | 0.668 | 0.628 | 0.466 | 0.628 | 0.408 | - |

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 [9]. 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 [10]. 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 [11]. 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 [12]. 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

Path | Path coefficient | |||
---|---|---|---|---|

Boy | Girl | Critical ratio | Difference test (P value) | |

1 | 0.36 | 0.278 | −0.586 | >0.05 |

2 | 0.882 | 0.678 | −2.131 | >0.05 |

3 | 0.126 | 0.122 | −0.075 | >0.05 |

4 | 0.181 | 0.288 | 2.04 | >0.05 |

Path | Path coefficient | |||
---|---|---|---|---|

Primary level | Senior grades | Critical ratio | Difference test (P value) | |

1 | 0.224 | 0.431 | 1.587 | >0.05 |

2 | 0.731 | 0.635 | 1.442 | >0.05 |

3 | 0.082 | 0.156 | 1.236 | >0.05 |

4 | 0.308 | 0.224 | 1.766 | >0.05 |

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

Path | Path coefficient | |||
---|---|---|---|---|

Boy | Girl | Critical ratio | Difference test (P value) | |

1 | 0.36 | 0.278 | −0.586 | >0.05 |

2 | 0.882 | 0.678 | −2.131 | >0.05 |

3 | 0.126 | 0.122 | −0.075 | >0.05 |

4 | 0.181 | 0.288 | 2.04 | >0.05 |

#### Mean, standard deviation, and difference comparison of scores for each test variable

Test variable | Gender | ||
---|---|---|---|

Male | Female | F | |

Exercise atmosphere | 55.51±6.91 | 51.45±7.65 | 0.27 |

Exercise motivation | 51.26±9.95 | 44.79±10.82 | 1.71 |

Self-management | 65.87±12.57 | 61.15±12.04 | 0.08 |

Method management | 10.22±6.45 | 27.41±6.55 | 0.09 |

Time management | 12.81±1.14 | 11.92±1.21 | 0.06 |

Content management | 10.92±2.57 | 9.98±2.58 | 0.51 |

Motivation management | 11.90±2.19 | 11.81±2.16 | 0.51 |

Persistence | 20.88±4.62 | 16.89±5.62 | 6.44 |

#### Pearson correlation analysis for each variable

Test variable | 1) | 2) | 3) | 4) | 5) | 6) | 7) | 8) |
---|---|---|---|---|---|---|---|---|

1) Exercise atmosphere | - | |||||||

2) Exercise motivation | 0.514 | - | ||||||

3) Self-management | 0.512 | 0.635 | - | |||||

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 | - | ||

7)Motivation management | 0.316 | 0.421 | 0.614 | 0.468 | 0.266 | 0.516 | - | |

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 Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Research on sustainable design of sports centre based on algorithm verification Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data 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 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 Institutional investor company social responsibility report and company performance Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer 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 Informatisation of educational reform based on fractional differential equations Application research on piano teaching in colleges and universities based on remote wireless network communication Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method 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 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 Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the 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 A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control 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 Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations 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 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 Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm 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 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 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 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 H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model 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