Based on the differential equation verification method, this study explores the characteristic model of mental health education activities for all employees and provides further research basis for constructing the competency characteristics for all employees in mental health education colleges. The results show that (1) the competence characteristics of all psychological teachers in mental health education colleges include interpersonal understanding and communication, respect for students, student service orientation, self-regulation and control, self-confidence, desire for achievement, influence, promotion of student development, organisation and coordination, 12 characteristics of professional knowledge skills, analytical thinking and reflective ability, (2) these 12 characteristics can be summarised into 4 dimensions: help and service, personal effectiveness, management skills and cognitive dimensions and (3) 12 characteristics of the model. The top 5 in the ranking are interpersonal understanding and communication, self-regulation and control, respect for students, student service orientation and promotion of student development.

#### Keywords

- differential equations
- behavioural event interview method
- mental health education
- all-staff mentality teachers in colleges and universities

#### MSC 2010

- 97C20

Mental health education is a highly professional and demanding job. With the in-depth development of school mental health education, the quality and specialisation requirements for all mental health teachers in colleges and universities for mental health education are becoming higher and higher. A high-quality team of all-staff psychology teachers in colleges and universities who are competent for school mental health education has become the key to doing well in school psychological counselling. Therefore, it is particularly important to study the competency characteristics of all psychological teachers in mental health education colleges. More and more researches and practices have shown that, in order to do a good job of mental health education for students, we must attach great importance to the training of all-staff mentality teachers in mental health education colleges.

The Ministry of Education's ‘Several Opinions on Strengthening Psychological Health Education in Primary and Secondary Schools’ pointed out that doing a good job in the construction of the teaching staff and improving the mental health of all psychological teachers in colleges and universities is an important condition for ensuring the normal development of mental health education. To improve the mental health education level of students, it is necessary to improve the mental health education ability of all teachers in colleges and universities. However, the current situation in many mental health education colleges and universities in China is that all teaching positions are concurrently held by moral education workers. This has led to the low professionalisation of all mental health teachers in mental health education colleges and universities in China, and they have not passed strict personnel selection and professional training and hence lack relevant practical experience. Therefore, it is very important to find the key factors that lead to the effectiveness of mental health education and explore the selection and training of mental health education colleges and universities.

McClelland believes that competency refers to ‘the deep-seated characteristics of individuals that can distinguish outstanding accomplishers from mediocre performances in a certain job, including different motivational performance, personality traits, moral qualities, self-image, and social role characteristics [1]. Attitudes or values, and the level of knowledge and skills in a certain field.’ From the perspective of combining theory and empirical research, this study explores the differential equations of all-employee psychological teachers in mental health education colleges and universities and provides a reference for the recruitment and selection, training, performance evaluation and comprehensive quality evaluation.

The first stage: Combining the job responsibilities of all psychological teachers in mental health education colleges and universities and adopting the literature method and expert consultation method to determine the performance evaluation standards. Or all-member psychology teachers of provincial-level outstanding colleges and universities, outstanding educators, all-employee psychology teachers of model colleges and universities, advanced workers in the education system, etc. or all-member psychology teachers of colleges and universities who have been commended for outstanding achievements in mental health education at the national or provincial level 2) All college psychological teachers who have been engaged in mental health education for >4 years.

The second stage: According to the above evaluation criteria, 5 excellent performers and 5 ordinary performers are selected from all primary and secondary schools in Chongqing as interview subjects. The gender composition is 4 females in the excellent group and 1 male; and 4 females in the general group and 1 male. The school category is composed of 4 psychological teachers in the excellent group of middle schools and colleges, 1 psychological teacher in the elementary schools; and 4 psychological teachers in the general middle schools and colleges, and 1 psychological teacher in the primary schools. Then, the researchers conducted behavioural event interviews with the subjects, that is, the interviewees were asked to narrate their key cases in the mental health education work, including 3 successful events, unsuccessful events or negative events. The participants described in detail the cause, process, result, time, relevant people, the scope of the incident, level of influence and their own thoughts or feelings at the time and recorded the content of the interview [2].

The third stage: Organising the interview recordings into manuscripts and using Spencer's competency coding dictionary to encode the interview data. A coding team composed of two people respectively coded an interview recording manuscript. After the independent coding was completed, a comparative discussion was conducted to ensure that the two coders reached a consensus on the coding of the interview manuscript. After unifying the opinions, modify the competency rating scale to form a mental health education feature rating scale for all-staff mental health education activities, and then code and score all recorded texts, and use SPSS12.0 to analyse the data obtained by coding deal with.

Introducing the fractal space-time distance of the differential equation of one-dimensional space and time
_{0} = 0 is set and the one-dimensional problem source point coordinate _{j}

Without loss of generality, consider a particle moving along a one-dimensional curve in fractal time at a constant velocity. The relationship between movement distance and time is
_{0} is the initial moment and

The position of the particle motion expressed by Eq. (9) at time

According to the above analysis, it can be seen that the differential equation calculus and fractional calculus are intrinsically quantitatively related to the fractal dimension, that is, the order of the time differential equation calculus and fractional calculus is the time fractal dimension

From the perspective of time fractal analysis, differential equation calculus and fractional calculus are opposite processes. The former advances gradually from the initial moment, while the latter recursively from the end moment. From the time history analysis, there is a certain reverse correspondence between the two [3].

On the other hand, differential equation calculus is a local operator and fractional calculus is a non-local operator. Therefore, even if both are used to describe the fractal process, the corresponding statistical process is completely different. They are two different calculus operators. In addition, the geometric basis of the derivative equations of differential equations is the non-Euclidean differential equation fractal distance, while the geometric basis of the fractional calculus is still the Euclidean distance. The statistical mechanics background of the two is also completely different. The differential equation derivative diffusion equation model describes the spreading Gaussian distribution and the spreading exponential attenuation diffusion, while the fractional derivative diffusion equation describes the Levatich steady-state distribution and the ML attenuation diffusion. The comparison of exponential decay, stretch exponential relaxation and ML decay is shown in Figure 1.

The interview lengths of 10 interview texts were analysed and statistically compared. Among them, 5 were in the excellent group and 5 were in the ordinary group. The results are shown in Table 1.

The length of the interview.

1 | 5290 | 3766 | 3000 | 2100 |

2 | 4048 | 2454 | 2220 | 1740 |

3 | 2842 | 4382 | 1800 | 2340 |

4 | 4514 | 3104 | 2580 | 2280 |

5 | 3480 | 2701 | 1920 | 1740 |

In order to ensure that the differences in the competency characteristics between the excellent group and the ordinary group are not caused by the length of the interview, the number of words and interview time between the excellent group and the ordinary group was tested for significance. The results are shown in Table 2.

Interview length difference analysis.

Interview words/words | 4034.8 | 940.2 | 3281.4 | 790.42 | 8 | 1.372 | 0.207 |

Interview time/s | 2304 | 492.22 | 2040 | 287.75 | 8 | 1.035 | 0.331 |

Interview words/words | 4034.8 | 940.2 | 3281.4 | 790.42 | 8 | 1.372 | 0.207 |

Interview time/s | 2304 | 492.22 | 2040 | 287.75 | 8 | 1.035 | 0.331 |

The average word count of the excellent group interview was 4035 words and the average time was 2304 s; and the average word count of the ordinary group interview was 3281 words and the average time was 2040 s. The difference between the excellent group and the ordinary group in terms of interview text and interview time was not significant at the 0.05 level. It can be seen that the number of words and the length of time did not affect the difference in competency between the excellent group and the ordinary group.

After discussing and analysing the pre-coded text, the two coders agreed that they can learn from interpersonal understanding and communication, respect for students, sense of responsibility, student service orientation, enthusiasm, relationship establishment, self-regulation and control, self-confidence, initiative, desire for achievement, flexibility, influence, honesty and integrity, promotion of student development, career preferences, organisational coordination, professional knowledge and skills, information collection, analytical thinking, reflective ability, challenge and support, innovation and adaptability. These are 23 competency characteristics. It depends on whether all the psychological teachers of the mental health education colleges and universities have these competent characteristics [4].

The two coders formally coded and scored the interview recordings according to the coding dictionary of mental health education activities for all employees. The coding and scoring were performed independently, back to back. The degree of consistency of independent coding results for the same text is an important factor affecting the reliability of the competency evaluation method, and an important indicator of the reliability and objectivity of the coding results. In order to test whether the scores between the two coders are consistent, this study conducted the scorer reliability test which is shown in Table 3.

Scorer reliability analysis results.

Interpersonal understanding and communication | 0.851** | Honesty | 0.997** |

Respect students | 0.69* | Promote student development | 0.745* |

Sense of responsibility | 0.876** | Career preference | 0.874** |

Student service orientation | 0.737* | Organisation and coordination | 0.992** |

Enthusiasm | 0.88** | Professional knowledge and skills | 0.843** |

Relationship establishment | 0.848** | Collect message | 0.865** |

Self-regulation and control | 0.795** | Analytical thinking | 0.991** |

Self-confidence | 0.884** | Reflective ability | 0.851** |

Initiative | 0.955** | Challenge and support | 0.819** |

Desire for achievement | 0.963** | Innovation | 0.911** |

Flexibility | 0.751* | Resilience | 0.934** |

Influence | 0.985** | Overall consistency | 0.979** |

In Hay's classic research, three indicators, frequency, average grade score, and highest score, are used for statistical analysis. Among them, the average grade score is the best. Research by Shikan and others in China has also confirmed this result. This study mainly used two coders to test the average grade score of the text. The test results show that the two coders have a high degree of consistency in each competency, with an overall consistency of 0.979, which is higher than that in previous studies.

Using the average grade score as an indicator, the average scores of the two coders on each competency feature are calculated and then the average scores of the excellent group and the ordinary group on each competency feature to test the significance of the difference are compared. The results are shown in Table 4.

Characteristics of mental health education activities for all employees in mental health education.

Personal effectiveness | Self-regulation and control, self-confidence, desire for achievement, influence |

Management skills | Promote student development, organise and coordinate |

Cognitive dimension | Professional knowledge and skills, reflective ability, analytical thinking |

Help and service | Interpersonal understanding and communication, respect for students, student service orientation |

From the test results, it can be seen that the excellent group and the ordinary group have extremely significant differences in interpersonal understanding and communication, desire for achievement, influence and reflective ability. They are in respect of students, student service orientation, self-control and adjustment, self-confidence and there are significant differences in the promotion of student development, organisation and coordination, professional knowledge and skills, and analytical thinking; but there are no significant differences between the two groups in other competency characteristics. Therefore, the 12 competence characteristics of all psychological teachers in mental health education colleges are interpersonal understanding and communication, respect for students, student service orientation, self-regulation and control, self-confidence, desire for achievement, influence, promotion of student development, organisation and coordination, professional knowledge skills, analytical thinking and reflective ability. The test results also show that the average grade scores of excellent and ordinary people are not high in the competence of analytical thinking. Researchers believe that, on the one hand, it may be caused by the coder's scoring standards. On the other hand, in the key events described, the descriptions of outstanding performers and ordinary performers did not show the higher-level behaviours in the competency coding dictionary characteristics, and so the score is not high [5].

According to the test results of the difference of interview data, find out the competencies with significant differences, and determine the competencies of all psychological teachers in mental health education colleges as: interpersonal understanding and communication, respect for students, student service orientation, self-regulation and control, self-confidence 12 competency characteristics: heart, desire for achievement, influence, promotion of student development, organisation and coordination, professional knowledge and skills, analytical thinking and reflective ability. According to Spencer's classification of competency characteristics, many competency characteristics contained in the mental health education activity characteristic model of mental health education for all employees are divided into four competency characteristics dimensions. See Table 5.

Competency score difference test between excellent group and ordinary group.

Interpersonal understanding and communication | 5.6 | 1.19 | 2.7 | 0.27 | 5.295 | 0.005 |

Respect students | 3.32 | 0.41 | 2.7 | 0.27 | 2.818 | 0.023 |

Sense of responsibility | 3.5 | 0.5 | 3.14 | 0.22 | 1.475 | 0.179 |

Student service orientation | 5.2 | 1.3 | 3.6 | 0.74 | 2.385 | 0.044 |

Enthusiasm | 3.34 | 0.42 | 2.82 | 0.47 | 1.838 | 0.103 |

Relationship establishment | 3.3 | 0.45 | 2.86 | 0.22 | 1.976 | 0.084 |

Self-regulation and control | 4.8 | 1.44 | 3 | 0.61 | 2.571 | 0.033 |

Self-confidence | 4.9 | 0.82 | 3.5 | 0.5 | 3.255 | 0.012 |

Initiative | 4.1 | 0.96 | 3.5 | 0.5 | 1.238 | 0.251 |

Desire for achievement | 3.7 | 0.84 | 3.4 | 0.42 | 5.02 | 0.001 |

Flexibility | 3.4 | 0.42 | 2.94 | 0.38 | 1.824 | 0.106 |

Influence | 4.6 | 1.08 | 2.4 | 0.65 | 3.889 | 0.005 |

Honesty | 3.5 | 0.5 | 3.2 | 0.27 | 1.17 | 70.273 |

Promote student development | 5.32 | 0.84 | 4 | 0.35 | 3.226 | 0.012 |

Career preference | 3.9 | 0.55 | 3.3 | 0.45 | 1.897 | 0.094 |

Organisation and coordination | 3.6 | 0.55 | 2.5 | 0.71 | 2.75 | 0.025 |

Professional knowledge and skills | 4.74 | 0.8 | 3.3 | 0.57 | 3.281 | 0.011 |

Collect message | 4 | 0.71 | 3.4 | 0.55 | 1.5 | 0.172 |

Analytical thinking | 3.02 | 1.1 | 1.5 | 0.5 | 2.821 | 0.022 |

Reflective ability | 3.7 | 0.45 | 2.5 | 0.35 | 4.707 | 0.002 |

Challenge and support | 2.6 | 0.55 | 2.26 | 0.49 | 1.037 | 0.33 |

Innovation | 3.4 | 0.31 | 3.1 | 0.26 | 1.651 | 0.137 |

The total frequency of the mental health education activities of all the mental health education activities mentioned by the 10 subjects during the interview was ranked from high to low. The results are shown in Table 6.

Competency frequency statistics.

1 | Interpersonal understanding and communication | 33 | 7 | Self-confidence | 22 |

2 | Self-regulation and control | 30 | 8 | Professional knowledge and skills | 20 |

3 | Respect students | 28 | 9 | Reflective ability | 19 |

4 | Student service orientation | 27 | 10 | Analytical thinking | 18 |

5 | Promote student development | 25 | 11 | Organisation and coordination | 16 |

6 | Influence | 22 | 12 | Desire for achievement | 15 |

It can be seen from Table 6 that among the 12 features of the mental health education activity feature model for all employees of mental health education, interpersonal understanding and communication, self-regulation and control, respect for students, student service orientation, and promotion of student development appear more frequently than other features, which shows that for all psychological teachers in mental health education colleges and universities, these 5 characteristics are more important than other characteristics.

For example, the main requirements of the International School Psychology Association for school psychologists include mastering the core knowledge of psychology, developing professional decision-making capabilities, strengthening interpersonal communication skills, mastering design and research skills, understanding ethical knowledge and establishing professional values, and focusing on seeking problem-solving skills required for professional practice, etc. The research shows that the differential equations of the full-staff mental teachers in mental health education colleges and universities are consistent with the characteristics of professional knowledge and skills, interpersonal understanding and communication, student service orientation and analytical thinking ability. The research of Chen Hong and Ye Yadao shows that the competence of all-staff mental teachers in school mental health education should include the following aspects: possessing school mental health education concepts, possessing professional personality traits, solid professional knowledge, and possessing professional skills or abilities, professional duties and professional ethics, professional personality tendencies and self-identity. This shows that the judgement of the characteristics of mental health education activities for all employees in mental health education is relatively consistent in terms of professional knowledge and skills, self-confidence, student service orientation, respect for students and promotion of student development. Zeng Ling Juan's research believes that the competence characteristics of all psychological teachers in mental health education colleges can be summarised as professional philosophy and professional awareness, professional personality traits, professional knowledge and skills, etc. This is basically consistent with the conclusion of this research to a large extent [6, 7].

Xu Jianping's research also shows that the competencies of all psychological teachers of excellent colleges and universities include 11 features such as initiative, sense of responsibility, understanding of others, self-control, professional knowledge and skills, emotional awareness, challenge and support, self-confidence, conceptual thinking, self-assessment and efficiency. The competencies shared by all psychological teachers in colleges and universities include 11 characteristics such as organisation and management ability, integrity, creativity, tolerance, teamwork, reflection ability, professional preferences, communication skills, respect for others, analytical thinking and stable emotions. This research conclusion is basically consistent with the competency characteristics of interpersonal understanding and communication, professional knowledge and skills, self-regulation and control, self-confidence, respect for students, analytical thinking, reflective ability, organisation and coordination in this research; student service orientation, desire for achievement, influence and promotion of student development are the unique competency characteristics of all psychological teachers in mental health education colleges. This shows that professional knowledge and skills, interpersonal understanding and communication, self-regulation and control, self-confidence, respect for students, analytical thinking and other competency characteristics are the common competence characteristics of all college psychological teachers in this profession, and they serve as mental health education. All college psychological teachers also need to have the competence characteristics of student service orientation, desire for achievement, influence and promotion of student development. These are also key elements that must be possessed to do a good job of mental health education.

In this study, the mental health education activity characteristic model for all employees of mental health education includes four dimensions of help and service, personal effectiveness, management skills and cognition, with a total of 12 competency characteristics. The 12 competencies are interpersonal understanding and communication, respect for students, student service orientation, self-regulation and control, self-confidence, desire for achievement, influence, promotion of student development, organisation and coordination, professional knowledge and skills, analytical thinking and reflection ability. Among the 12 characteristics of the model, the top 5 are interpersonal understanding and communication, self-regulation and control, respect for students, student service orientation and promotion of student development.

#### Competency frequency statistics.

1 | Interpersonal understanding and communication | 33 | 7 | Self-confidence | 22 |

2 | Self-regulation and control | 30 | 8 | Professional knowledge and skills | 20 |

3 | Respect students | 28 | 9 | Reflective ability | 19 |

4 | Student service orientation | 27 | 10 | Analytical thinking | 18 |

5 | Promote student development | 25 | 11 | Organisation and coordination | 16 |

6 | Influence | 22 | 12 | Desire for achievement | 15 |

#### Interview length difference analysis.

Interview words/words | 4034.8 | 940.2 | 3281.4 | 790.42 | 8 | 1.372 | 0.207 |

Interview time/s | 2304 | 492.22 | 2040 | 287.75 | 8 | 1.035 | 0.331 |

#### Scorer reliability analysis results.

Interpersonal understanding and communication | 0.851** | Honesty | 0.997** |

Respect students | 0.69* | Promote student development | 0.745* |

Sense of responsibility | 0.876** | Career preference | 0.874** |

Student service orientation | 0.737* | Organisation and coordination | 0.992** |

Enthusiasm | 0.88** | Professional knowledge and skills | 0.843** |

Relationship establishment | 0.848** | Collect message | 0.865** |

Self-regulation and control | 0.795** | Analytical thinking | 0.991** |

Self-confidence | 0.884** | Reflective ability | 0.851** |

Initiative | 0.955** | Challenge and support | 0.819** |

Desire for achievement | 0.963** | Innovation | 0.911** |

Flexibility | 0.751* | Resilience | 0.934** |

Influence | 0.985** | Overall consistency | 0.979** |

#### The length of the interview.

1 | 5290 | 3766 | 3000 | 2100 |

2 | 4048 | 2454 | 2220 | 1740 |

3 | 2842 | 4382 | 1800 | 2340 |

4 | 4514 | 3104 | 2580 | 2280 |

5 | 3480 | 2701 | 1920 | 1740 |

#### Competency score difference test between excellent group and ordinary group.

Interpersonal understanding and communication | 5.6 | 1.19 | 2.7 | 0.27 | 5.295 | 0.005 |

Respect students | 3.32 | 0.41 | 2.7 | 0.27 | 2.818 | 0.023 |

Sense of responsibility | 3.5 | 0.5 | 3.14 | 0.22 | 1.475 | 0.179 |

Student service orientation | 5.2 | 1.3 | 3.6 | 0.74 | 2.385 | 0.044 |

Enthusiasm | 3.34 | 0.42 | 2.82 | 0.47 | 1.838 | 0.103 |

Relationship establishment | 3.3 | 0.45 | 2.86 | 0.22 | 1.976 | 0.084 |

Self-regulation and control | 4.8 | 1.44 | 3 | 0.61 | 2.571 | 0.033 |

Self-confidence | 4.9 | 0.82 | 3.5 | 0.5 | 3.255 | 0.012 |

Initiative | 4.1 | 0.96 | 3.5 | 0.5 | 1.238 | 0.251 |

Desire for achievement | 3.7 | 0.84 | 3.4 | 0.42 | 5.02 | 0.001 |

Flexibility | 3.4 | 0.42 | 2.94 | 0.38 | 1.824 | 0.106 |

Influence | 4.6 | 1.08 | 2.4 | 0.65 | 3.889 | 0.005 |

Honesty | 3.5 | 0.5 | 3.2 | 0.27 | 1.17 | 70.273 |

Promote student development | 5.32 | 0.84 | 4 | 0.35 | 3.226 | 0.012 |

Career preference | 3.9 | 0.55 | 3.3 | 0.45 | 1.897 | 0.094 |

Organisation and coordination | 3.6 | 0.55 | 2.5 | 0.71 | 2.75 | 0.025 |

Professional knowledge and skills | 4.74 | 0.8 | 3.3 | 0.57 | 3.281 | 0.011 |

Collect message | 4 | 0.71 | 3.4 | 0.55 | 1.5 | 0.172 |

Analytical thinking | 3.02 | 1.1 | 1.5 | 0.5 | 2.821 | 0.022 |

Reflective ability | 3.7 | 0.45 | 2.5 | 0.35 | 4.707 | 0.002 |

Challenge and support | 2.6 | 0.55 | 2.26 | 0.49 | 1.037 | 0.33 |

Innovation | 3.4 | 0.31 | 3.1 | 0.26 | 1.651 | 0.137 |

#### Characteristics of mental health education activities for all employees in mental health education.

Personal effectiveness | Self-regulation and control, self-confidence, desire for achievement, influence |

Management skills | Promote student development, organise and coordinate |

Cognitive dimension | Professional knowledge and skills, reflective ability, analytical thinking |

Help and service | Interpersonal understanding and communication, respect for students, student service orientation |

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training using calculus method Engineering project management based on multiple regression equation and building information modelling technology 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 Mathematical model of back propagation for stock price forecasting Application of regression function model based on panel data in bank resource allocation financial risk management Application of Logical Regression Function Model in Credit Business of Commercial Banks 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 Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching 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 Application of Lane-Emden differential equation numerical method in fair value analysis of financial accounting Regression function model in risk management of bank resource allocation Application of numerical method of functional differential equations in fair value of financial accounting Optimal solution of fractional differential equations in solving the relief of college students’ mental obstacles Risk contagion in financial markets based on copula model Calculating university education model based on finite element fractional differential equations and macro-control analysis Automatic parameter selection ZVD shaping algorithm for crane vibration suppression based on particle swarm optimisation 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 Calculation of tourism development income index based on finite element ordinary differential mathematical equation Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Radar system simulation and non-Gaussian mathematical model under virtual reality technology Comparison of compression estimations under the penalty functions of different violent crimes on campus through deep learning and linear spatial autoregressive models Research and application of constructing football training linear programming based on multiple linear regression equation Research on management evaluation of enterprise sales cash flow percentage method based on the application of quadratic linear regression equations Mathematical simulation analysis of optimal detection of shot-putters’ best path Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Mathematical modelling of enterprise financial risk assessment based on risk conduction model Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Mathematical simulation experiment based on optimisation of heat treatment process of aluminium alloy materials Mathematical model of transforming image elements to structured data based on BP neural network Educational reform informatisation based on fractional differential equation 3D Mathematical Modelling Technology in Visual Rehearsal System of Sports Dance 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 Informationisation of teaching model for track and field education based on finite element higher-order fractional differential equation Information technology of preschool education reform of fine arts based on fractional differential equation Information Teaching Model of Preschool Art Education in Colleges and Universities Based on Finite Element Higher-Order Fractional Differential Equation Application of artificial intelligence algorithm in mathematical modelling and solving College Students’ Mental Health Climbing Consumption Model Based on Nonlinear Differential Equations Communication architecture of power monitoring system based on incidence matrix model Differential equation to verify the validity of the model of the whole-person mental health education activity in Universities Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Analysis and Prediction of College Students’ Mental Health Based on K-means Clustering Algorithm Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement Energy-saving technology of BIM green buildings using fractional differential equation Study on the training model of football movement trajectory drop point based on fractional differential equation Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation User online consumption behaviour based on fractional differential equation Differential equation model of financial market stability based on Internet big data Multi-attribute Decision Method Based on Normal Random Variable in Economic Management Risk Control Children’s cognitive function and mental health based on finite element nonlinear mathematical model 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 Stock price analysis based on the research of multiple linear regression macroeconomic variables Fractional Linear Regression Equation in Agricultural Disaster Assessment Model Based on Geographic Information System Analysis Technology