The influence of learning emotions on learning behaviors in college physical education is directly reflected in learning efficiency. Based on this research background, the paper applies a mathematical, statistical model to structural equation modeling of the emotional situation of students in a school's physical education curriculum. The study results found that college students have lower positive emotional attitudes towards college physical education courses. Thus, students’ mood is affected by the. For this reason, we should eliminate students’ resistance and fear of college physical education courses and promptly correct students’ unhealthy learning emotions about college physical education courses. In this way, it helps students correct their negative feelings about college physical education courses.

#### Keywords

- Learning mood
- college physical education curriculum
- structural equation
- mathematical-statistical model

#### MSC 2010

- 62J10

The current physical education curriculum, professional talent training, teaching reform research, students’ learning mood, and influencing factors of college physical education curriculum have attracted many scholars’ attention. Learning emotion refers to the psychological state of students’ understanding of learning and emotions. It has regulatory significance for learning behavior. Therefore, how to cultivate students to form correct and positive learning emotions and then improve their learning behaviors and results has always been a critical concern in pedagogy [1]. Unfortunately, there are still few domestic types of research on students’ emotions related to college physical education courses. The existing literature mainly focuses on studying related courses such as psychological statistics, medical statistics, and mathematics. Still, their analysis methods are mostly limited to descriptive analysis and regression analysis.

“Learning emotions” are not directly observable. Therefore, it needs to be measured by a scale. So far, there are more than ten kinds of leaves about learning emotions in college physical education courses. Foreign scholars widely adopt the SATS scale (Survey of Attitudes Toward Statistics). Schau proposed the scale in 1995, and initially, there were only 28 measurement items (SATS-28). Later the plate was added to 36 measurement items (SATS-36). This article will combine the SATS scale design questionnaire to carry out a field survey of college students in a sports college [2]. We measure their learning emotions towards college physical education courses. We build a learning emotion model based on the project packaging method and high-order factor structural equations to establish an overall understanding of college students’ learning emotions in college physical education courses. The thesis studies the influence path and influence intensity between college students’ college physical education curriculum learning emotions, physical ability, and expected mastery. The research conclusions of this article are expected to play a guiding role in the teaching activities of college physical education courses.

We use the SATS-36 scale to measure the emotions of college students in college physical education courses. The scale adopts a 7-level Likert plate (1 means “strongly disagree,” 7 means “strongly agree,” and so on). Thus, we use 6 dimensions, including emotion, cognitive ability, value, difficulty, interest, and effort, to measure the “emotion of college physical education courses.” In addition, the research also includes the factors of “sports ability” and “expected mastery” (as shown in Table 1).

Eight potential factors.

Latent factor | meaning | Number of Questions | Examples of measurement questions |
---|---|---|---|

emotion | Positive or negative feelings about the physical education curriculum | 6 | Q3: I will like sports. |

cognitive ability | Views on their ability to apply sports knowledge and skills | 6 | Q31: I can learn sports. |

value | Views on the value of sports knowledge in life and work | 9 | Q9: Physical education should be a necessary part of professional training. |

Difficulty | Awareness of the problem of physical education courses | 7 | Q6: The sports formula is easy to understand. |

interest | Interest in physical education | 4 | Q20: I am very interested in using sports. |

Work hard | The effort you intend to make for the physical education curriculum | 4 | Q14: I plan to study hard for every physical education test. |

Expected mastery | Anticipate their level of ability of sports knowledge | 2 | Q40: How confident are you in mastering the basics of sports? |

Physical ability | Past sports level | 2 | Q37: In the physical education courses you have taken before, how did you score? |

Structural equation modeling (SEM) is also often referred to as structural equation modeling. SEM is a statistical method to analyze the relationship between variables based on the covariance matrix of the variables. It can process latent variables and their measurement indicators at the same time. Simply put, the structural equation model can be divided into two parts: measurement model and structural model. The former describes the relationship between latent variables and measurement indicators, and the latter describes the relationship between latent variables [3]. The following measurement equation usually expresses the relationship between measurement indicators and latent variables:

Among them _{x} is the factor loading matrix of the exogenous measurement index on the exogenous latent variable, which represents the relationship between the exogenous measurement index and the exogenous latent variable. ∧_{y} is the factor loading matrix of the endogenous measurement index on the endogenous latent variable, representing the relationship between the endogenous measurement index and the endogenous latent variable.

High-order confirmatory factor analysis (HCFA) is also known as the full Y model. The core idea is to coordinate the primary factors through high-level factors, thereby simplifying the correlation between the primary factors [5]. An HCFA model only needs to be determined by the following two equations:

When there is a consistent high correlation between the first-order factors, high-order confirmatory factor analysis can often achieve better results.

The item combination method is a process of reintegrating two or more question items in the same scale and using the composite score (total score or average) as the score of the new index to analyze. For example, a scale originally had 9 question items. We can use each 3 question item to calculate its composite score to obtain 3 new indicators and then use these 3 new indicators for subsequent analysis.

Some scholars have shown that the project portfolio method can correct the non-normality of the data to a certain extent. When we reduce the number of parameters to be estimated, we can effectively avoid problems such as multicollinearity between measurement indicators, excessive error correlation, and cross-loading of measurement indicators from adversely affecting the model. Furthermore, this method can improve the fitting effect of higher-order factor models. Some scholars have proposed a two-stage simplification method that combines project portfolio and high-order factor analysis [6]. This method can significantly simplify the model and obtain the perfect goodness of fit. It is especially suitable for the situation with many model parameters.

This article adopts the project portfolio method to form higher-order factors of learning emotion. This article has six potential first-order factors (emotion, cognitive ability, value, difficulty, interest, effort), as shown in Table 1. We take the arithmetic average of each factor's measured variables as the value of the element. The original six first-order factors become “explicit variables” (AFFPC, COGPC, VALPC, DIFPC, INTPC, and EFFPC) and jointly measure the “attitude “High-order factor (ATTITUDE). The “attitude” high-level factor will further affect the “expected mastery” factor (EXPMSTRY), and it will be affected by the “sports ability” factor (MATHCOMP). At the same time, “sports ability” will also directly affect the “expected mastery” (as shown in Figure 1).

In theory, the more active the learning mood of university physical education courses, the easier it is to expect that one has a good grasp of statistical knowledge. The stronger the physical ability, the more confident they are in their physical fitness [7]. This also often leads to the better the expected mastery of the physical education curriculum. In addition, the stronger the physical ability, the easier it is to get a sense of accomplishment from similar courses. The easier it is for students to take a positive attitude towards university physical education courses. Therefore, this article proposes the following hypotheses:

H1: “Attitude” positively affects “expected mastery.”

H2: “Sports ability” positively affects “expected mastery.”

H3: “Sports ability” positively affects “attitude.”

This study designed the questionnaire based on the English-Chinese version of the SATS-36 scale. The questionnaire consists of 47 items, including 36 Likert scale items and 11 background information items. The survey subjects are all the sophomore students who participated in physical education courses in a sports college [8]. The questionnaire was issued before the first class at the beginning of the semester. After preprocessing, such as deleting wrong values, filling in missing values, and deleting outliers, we finally get data containing 1074 sample points. Among them, girls accounted for 60.99%. Thus, the composition of the sample is consistent with the actual situation of sports colleges.

We use R software for statistical analysis. Table 2 gives the mean value of each factor. Among them, the value of each element itself is obtained by taking the mean value of its corresponding measurement item to get 1. It can be seen that the average values of the other factors except the difficulty factor are all greater than 4. That is to say, the overall emotions of the students towards the university physical education courses are positive [9]. Among them, the two factors of value and effort have the most considerable mean value. Students must recognize the importance of university physical education courses and are willing to make more extraordinary efforts. Students generally have a strong interest in university physical education courses and typically hold a more positive attitude towards their cognitive abilities. And students have positive feelings about college physical education courses. According to the calculation of the mean value of the difficulty factor, it is found that most students think college physical education courses are challenging. In addition, students also have a positive attitude towards their physical ability and expected mastery.

Descriptive analysis of potential factors.

Latent factor | First-order factor/measurement item | The first-order factor/mean of the measurement items | Latent factor |
---|---|---|---|

Attitude | emotion | 4.649 | 4.816 |

cognitive ability | 4.854 | ||

value | 5.687 | ||

Difficulty | 3.088 | ||

interest | 4.919 | ||

Work hard | 5.67 | ||

Physical ability | Previous physical education results (Q37) | 4.28 | 4.252 |

Sports level (Q38) | 4.224 | ||

Expected mastery | Confidence in mastering sports knowledge (Q40) | 4.858 | 4.482 |

What kind of results are expected (Q44) | 4.105 |

We perform confirmatory factor analysis on the “attitude” factor measurement model, and the initial fitting results are given in the “initial results” row of Table 3. The standardized chi-square and each appropriate index have not reached the ideal outcome. Therefore, we need to modify the initial model: add error-related terms according to the adjustment index. The “adjusted result” row of Table 3 shows the fit of the adjusted model. The standardized chi-square value has been dramatically improved, and each fitting index meets the requirements of empirical criteria. Sports ability and expected mastery have to sound appropriate effects.

The initial fit index of the “attitude” factor measurement model.

Fitting effect | Initial result | Adjusted result | Rule of thumb | |
---|---|---|---|---|

Index | Chisq. | 503.816 | 11.146 | – |

df. | 9 | 3 | – | |

Chisq./df. | 55.98 | 3.715 | <3 | |

SRMR | 0.108 | 0.02 | <0.1 | |

RMSEA | 0.226 | 0.05 | <0.05 | |

CFI | 0.771 | 0.996 | >0.9 | |

GFI | 0.846 | 0.997 | >0.9 | |

NFI | 0.768 | 0.995 | >0.9 | |

IFI | 0.771 | 0.996 | >0.9 |

Table 4, the “Standardized Load Factor” column, gives the estimated results of the adjusted measurement model. In terms of the positive and negative coefficients, except for the difficulty factor, the other five first-order factors have positive loading coefficients on the “attitude” high-order factors. This result indicates that the more positive learning emotions mean, the more positive emotions are, the more willing to work hard to study university physical education courses [10]. The negative loading of the difficulty factor means a more positive attitude towards university physical education courses. The more students who often accompany this result agree with the difficulty of college physical education courses.

Confirmatory factor analysis estimation results.

Latent factor | First-order factor/measurement item | Standardized load factor |
---|---|---|

Attitude | Emotion | 0.678^{***} |

Cognitive ability | 0.745^{***} | |

Value | 0.706^{***} | |

Difficulty | −0.152^{***} | |

Interest | 0.601^{***} | |

Work hard | 0.524^{***} | |

Sports performance | Previous physical education results (Q37) | 0.917^{***} |

Sports level (Q38) | 0.951^{***} | |

Expected mastery | Confidence in mastering statistical knowledge (Q40) | 0.748^{***} |

What kind of results are expected (Q44) | 0.660^{***} |

Note:

means p <0.001.

From the significance of the coefficients, all loads are significant. Except for the first-order factor of difficulty, the absolute values of the load coefficients of the other six first-order factors on the second-order factors of attitude are more significant than 0.50. Among them, philosophy has the most muscular interpretation of cognitive ability, while understanding value, emotion, interest, and effort weakened in turn.

Table 5 shows the reliability and validity test of the questionnaire data. Attitude and sports ability belong to high reliability. The Cronbach alpha coefficient value of the expected mastery level is slightly lower but still acceptable. We then test the convergent validity and discriminative validity of the three factors. First, according to the study in Table 4, it is found that the load coefficients of each measurement index and its corresponding element are all significant, indicating that the questionnaire data has good convergence validity [11]. Secondly, from the average variation extraction amount (AVE) in Table 5, the sports ability factor is more significant than 0.5, and the mastery degree factor is expected to be close to 0.5. Thus, although the attitude factor is slightly lower, the overall convergence validity of the model is better. Finally, the correlation coefficient between attitude and expected mastery is somewhat higher than the

Reliability and validity test indicators.

Latent factor | Cronbach | AVE | Correlation coefficient | |||
---|---|---|---|---|---|---|

Attitude | Expected mastery | Physical ability | ||||

attitude | 0.739 | 0.362 | 0.602 | 1 | 0.789 | 0.434 |

Expected mastery | 0.624 | 0.498 | 0.705 | 0.789 | 1 | 0.81 |

Physical ability | 0.931 | 0.872 | 0.934 | 0.434 | 0.81 | 0 |

The structural equation fitting index of the theoretical model is shown in Table 6. Except for standardized chi-square and RMSEA, all other indicators are ideal. The estimated results of the structural model are shown in Table 7. First of all, from the positive and negative path coefficients, students’ learning emotions towards college physical education courses have a significant and greater positive impact on their expected mastery. The more positive the students are about college physical education courses, the better they will be expected. Sports ability has a significant and greater positive impact on the scheduled mastery and the learning mood of university physical education courses. The stronger the physical capacity, the easier it is for students to attitude towards university physical education courses positively. Secondly, students expect that they will also have a good grasp of physical education courses [12]. Therefore, the estimation result of the model supports the hypothesis H1~H3. Secondly, from the perspective of influence path and size, the attitude has a large and significant favorable influence on the degree of expectation mastery. Sports ability, directly and indirectly, affects the degree of expected knowledge through two paths. Its direct effect is 0.577, the indirect impact is 0.234 (0.434 × 0.539), and the total product is 0.810. This result shows more remarkable than the influence of attitude on the expected degree of mastery. This indicates that the students’ existing physical level is an essential factor in their judgment of the predicted mastery degree. The degree of influence of this factor is greater than the impact of students’ subjective attitudes towards college physical education courses.

Fitting index of structural equation model.

Fitting effect | Index | ||||||||
---|---|---|---|---|---|---|---|---|---|

Chisq. | df. | Chisq./df. | SRMR | RMSEA | CFI | GFI | NFI | IFI | |

Value | 245.15 | 26 | 9.429 | 0.06 | 0.089 | 0.957 | 0.957 | 0.953 | 0.957 |

Rule of thumb | – | – | <3 or <5 | <0.1 | <0.05 | >0.9 | >0.9 | >0.9 | >0.9 |

Estimation results of the structural equation model.

path | Standardized path coefficient | test result |
---|---|---|

Attitude β Sports Ability | 0.434^{***} | H1 established |

Expected mastery β sports ability | 0.577^{***} | H2 established |

Expected mastery β attitude | 0.539^{***} | H3 established |

Note:

means p <0.001.

With the development of data science, university physical education courses have become compulsory courses for finance and economics majors. Through this survey, it can be seen that most of the students have favorable emotions towards the study of university physical education courses and recognize the value of statistical knowledge [13]. Students have a strong interest in learning physical education and are willing to make more extraordinary efforts. They hold a positive attitude towards their cognitive abilities and expect to achieve better results. At the same time, it is undeniable that most physical education students think that college physical education courses are demanding, which may be related to the thinking mode and reasoning ability involved in the learning process. Therefore, the teaching process should focus on the students’ cognition of the difficulty of college physical education courses. We need to adopt appropriate teaching methods to make it easier and to eliminate students’ fear of college physical education courses as much as possible.

When students recognize the value of university physical education courses and have more positive emotions for studying university physical education courses, students will have the stronger motivation and a more positive attitude to research university physical education courses. At the same time, when students are more affirmed of their cognitive abilities and are more willing to work hard, it also means that students have a more positive attitude towards studying university physical education courses. Therefore, in the teaching process, teachers should emphasize to students the application value of physical fitness in real life and realize the importance of sports knowledge [14]. At the same time, teachers should adopt vivid teaching methods to mobilize students’ interest in learning and enhance students’ positive attitudes towards their cognitive abilities. In this way, teachers can encourage students to learn sports knowledge with a more positive attitude.

Students’ learning emotions towards college physical education courses positively influence their expected mastery. When students have a more positive attitude towards the study of university physical education courses, the more interested they are in university physical education courses, the more willing they are to make efforts–more excellent results.

Students’ physical quality significantly positively affects their learning mood of university physical education courses and their expected mastery of university physical education courses. The higher the student's material quality, the easier it is to obtain a sense of accomplishment from the study of physical education courses and then have a more superior sense of superiority in the face of college physical education courses [15]. The student's physical fitness will also directly affect the student's expected mastery. The stronger the physical ability, the more students will hope to achieve good university physical education courses.

Past physical exercise learning experience affects students’ expectations of college physical education courses. Therefore, on the one hand, teachers need to correct students’ emotions about physical education as soon as possible, and help them gain a sense of accomplishment from physical education learning will help cultivate students’ positive emotions for college physical education courses. However, on the other hand, teachers only can students improve their opposing expectations of college physical education courses.

Combined with the SATS-36 scale, we conducted a field investigation on the learning mood of college physical education courses of college students in a sports college in China. We use the project-based packaging method and the high-order factor method to construct a structural equation model about learning mood, sports level, and expected mastery. According to our research, the overall attitude of students towards college physical education courses is positive, but college physical education courses are considered problematic. Students’ attitudes towards college physical education courses are mainly reflected in five dimensions: emotion, cognitive ability, value, interest, and effort. Students’ learning emotions towards college physical education courses have a strong positive influence on their expected mastery. In addition, a student's physical fitness level can directly or indirectly affect their expected knowledge of college physical education courses.

#### Descriptive analysis of potential factors.

Latent factor | First-order factor/measurement item | The first-order factor/mean of the measurement items | Latent factor |
---|---|---|---|

Attitude | emotion | 4.649 | 4.816 |

cognitive ability | 4.854 | ||

value | 5.687 | ||

Difficulty | 3.088 | ||

interest | 4.919 | ||

Work hard | 5.67 | ||

Physical ability | Previous physical education results (Q37) | 4.28 | 4.252 |

Sports level (Q38) | 4.224 | ||

Expected mastery | Confidence in mastering sports knowledge (Q40) | 4.858 | 4.482 |

What kind of results are expected (Q44) | 4.105 |

#### Eight potential factors.

Latent factor | meaning | Number of Questions | Examples of measurement questions |
---|---|---|---|

emotion | Positive or negative feelings about the physical education curriculum | 6 | Q3: I will like sports. |

cognitive ability | Views on their ability to apply sports knowledge and skills | 6 | Q31: I can learn sports. |

value | Views on the value of sports knowledge in life and work | 9 | Q9: Physical education should be a necessary part of professional training. |

Difficulty | Awareness of the problem of physical education courses | 7 | Q6: The sports formula is easy to understand. |

interest | Interest in physical education | 4 | Q20: I am very interested in using sports. |

Work hard | The effort you intend to make for the physical education curriculum | 4 | Q14: I plan to study hard for every physical education test. |

Expected mastery | Anticipate their level of ability of sports knowledge | 2 | Q40: How confident are you in mastering the basics of sports? |

Physical ability | Past sports level | 2 | Q37: In the physical education courses you have taken before, how did you score? |

#### Reliability and validity test indicators.

Latent factor | Cronbach | AVE | Correlation coefficient | |||
---|---|---|---|---|---|---|

Attitude | Expected mastery | Physical ability | ||||

attitude | 0.739 | 0.362 | 0.602 | 1 | 0.789 | 0.434 |

Expected mastery | 0.624 | 0.498 | 0.705 | 0.789 | 1 | 0.81 |

Physical ability | 0.931 | 0.872 | 0.934 | 0.434 | 0.81 | 0 |

#### Estimation results of the structural equation model.

path | Standardized path coefficient | test result |
---|---|---|

Attitude β Sports Ability | 0.434^{***} | H1 established |

Expected mastery β sports ability | 0.577^{***} | H2 established |

Expected mastery β attitude | 0.539^{***} | H3 established |

#### The initial fit index of the “attitude” factor measurement model.

Fitting effect | Initial result | Adjusted result | Rule of thumb | |
---|---|---|---|---|

Index | Chisq. | 503.816 | 11.146 | – |

df. | 9 | 3 | – | |

Chisq./df. | 55.98 | 3.715 | <3 | |

SRMR | 0.108 | 0.02 | <0.1 | |

RMSEA | 0.226 | 0.05 | <0.05 | |

CFI | 0.771 | 0.996 | >0.9 | |

GFI | 0.846 | 0.997 | >0.9 | |

NFI | 0.768 | 0.995 | >0.9 | |

IFI | 0.771 | 0.996 | >0.9 |

#### Confirmatory factor analysis estimation results.

Latent factor | First-order factor/measurement item | Standardized load factor |
---|---|---|

Attitude | Emotion | 0.678^{***} |

Cognitive ability | 0.745^{***} | |

Value | 0.706^{***} | |

Difficulty | −0.152^{***} | |

Interest | 0.601^{***} | |

Work hard | 0.524^{***} | |

Sports performance | Previous physical education results (Q37) | 0.917^{***} |

Sports level (Q38) | 0.951^{***} | |

Expected mastery | Confidence in mastering statistical knowledge (Q40) | 0.748^{***} |

What kind of results are expected (Q44) | 0.660^{***} |

#### Fitting index of structural equation model.

Fitting effect | Index | ||||||||
---|---|---|---|---|---|---|---|---|---|

Chisq. | df. | Chisq./df. | SRMR | RMSEA | CFI | GFI | NFI | IFI | |

Value | 245.15 | 26 | 9.429 | 0.06 | 0.089 | 0.957 | 0.957 | 0.953 | 0.957 |

Rule of thumb | – | – | <3 or <5 | <0.1 | <0.05 | >0.9 | >0.9 | >0.9 | >0.9 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network 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 Performance evaluation of college laboratories based on fusion of decision tree and BP neural network 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 The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data 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 TOPSIS missile target selection method supported by the posterior probability of target recognition Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model The incentive contract of subject librarians in university library under the non-linear task importance Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot Visual error correction of continuous aerobics action images based on graph difference function Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Radioactive source search problem and optimisation model based on meta-heuristic algorithm 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 Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest 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 Data mining of Chain convenience stores location The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Parameter Id of Metal Hi-pressure State Equation 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 Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Application of regression function model based on panel data in bank resource allocation financial risk management Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis 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 Badminton players’ trajectory under numerical calculation method 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 Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Study of a linear-physical-programming-based approach for web service selection under uncertain service quality A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China 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 Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Good congruences on weakly U-abundant semigroups Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Mathematical simulation analysis of optimal detection of shot-putters’ best path 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 Nonlinear Differential Equations in the Teaching Model of Educational Informatisation Fed-UserPro: A user profile construction method based on federated learning The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption MCM of Student’s Physical Health Based on Mathematical Cone Attitude control for the rigid spacecraft with the improved extended state observer 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 Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast 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 Informatisation of educational reform based on fractional differential equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis 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 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression System dynamics model of output of ball mill 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 Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement 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 Design of Morlet wavelet neural network to solve the non-linear influenza disease system 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 Motion about equilibrium points in the Jupiter-Europa system with oblateness Fractional Differential Equations in Electronic Information Models Badminton players’ trajectory under numerical calculation method BIM Engineering Management Oriented to Curve Equation Model Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method 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 Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching 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 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 Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development 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 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 Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model