This article uses the gray system theory of nonlinear mathematical equations to predict the best results of China's track and field events in the 2021 Olympic Games. And compare the above prediction information with the track and field performance of the 2021 Olympic Games. The article uses this to guide the teaching of Chinese track and field sports and analyze the relevant factors affecting Chinese track and field training.

#### Keywords

- track and field sports
- nonlinear mathematics
- grey system theory
- science teaching
- 2021 Olympics
- performance prediction
- influencing factors

#### MSC 2010

- 93C10

Track and field sports are the foundation of competitive sports and an important part of the Olympic Games. However, China has won only a handful of gold medals in track and field events in the recent Olympic Games [1]. In the 2021 Olympic Games, which Chinese track and field events can enter the top 8, top 3, or win gold? What are the factors affecting the development of Chinese track and field sports? These questions are the research purpose of this article.

The article takes the first Place in Chinese track and field from 1999 to 2021 and the first, third, and eighth Place in track and field events of the recent six Olympic Games (except for the male and female m and m relay events) research objects [2].

In writing this article, I consulted many academic papers, newspapers and magazines, and other materials related to prediction, grey system theory, and track and field performance analysis [3].

We logically summarize the statistical results. It analyzes the current situation and development trend of the overall athletic level of men and women in Chinese track and field events from 1999 to 2021.

We summarize and organize the collected data and use Spss 16.0 and Matlab software for statistical analysis and comparison. Statistical diagnosis is to diagnose the whole process of solving problems by statistical inference methods, and impact analysis is a very important branch of statistical diagnosis [4]. At present, the research on the statistical diagnosis of linear regression models has been very in-depth. There are also some research results on the diagnosis methods of nonlinear models and generalized linear models. This paper systematically studies its statistical diagnosis and impact analysis methods by aiming at the widely used Poisson regression model. Consider the following model. Suppose _{i}_{1}, _{2},⋯_{p}^{T} is an unknown parameter. Equation (2) is called the Poisson regression model. If we assume _{1}, _{2},⋯_{n}^{T}, _{1}, _{2},⋯_{n}^{T}, _{1}, _{2},⋯ _{n}^{T}, the vector form of the Poisson regression model is: _{1}, _{2},⋯_{n}

The accuracy of prediction is the accuracy of prediction, which is used to describe the numerical performance of the degree of deviation between the predicted value and the actual value [5]. The accuracy of the gray prediction method is verified by comparing the results of the men's and women's first place in the track and field events of the 2021 Olympic Games with the predicted results. The average error rate of 4 of the 36 men's and women's track and field events in the 2021 Olympic Games is >5%, while the average error rate of the other 32 events is between 1% and 5%. By further calculating, the average error rate is 1.50%, not >2% (Table 1). This shows that the gray prediction method has a high prediction accuracy for the entire sample. It can predict the first Place in Chinese track and field in 2021 and the first, third, and eighth Place in the Olympic track and field.

2021 Chinese Men's and Women's No. 1 and Olympic Games No. 1, 3, 8 Predictions

Man | Woman | Man | Woman | Man | Woman | |
---|---|---|---|---|---|---|

9.87 | 11.01 | 9.98 | 11.26 | |||

19.84 | 22.27 | 20.03 | 21.28 | |||

43.92 | 49.39 | 44.73 | 49.67 | 1 | ||

01:44.9 | 01:56.7 | 01:44.9 | 01:56.8 | 8 | 1 | |

03:32.6 | 03:55.6 | 03:32.8 | 04:08.8 | |||

08:13.7 | 08:14.4 | |||||

110 mH | 12.91 | 12.52 | 13.13 | 12.59 | 1 | |

44.95 | 52.74 | 48.3 | 53.3 | 8 | 8 | |

13:24.9 | 13:24.4 | |||||

27:01.4 | 27:11.8 | |||||

0.0433565 | 01:20.4 | 1 | ||||

3:40:23 | 3:49:36 | 1 | ||||

2:10:52 | .2:24.36 | 2:12:09 | 2:26:24 | 1 | ||

20.75 | 19.11 | 20.71 | 18.84 | 8 | 8 | |

68.76 | 67.46 | 67.23 | 64.15 | 8 | 3 | |

89.22 | 68.53 | 87.96 | 63.93 | |||

80.402 | 78.61 | |||||

2.36 | 2.05 | 2.32 | 2.02 | 8 | 8 | |

8.49 | 6.95 | 8.32 | 6.9 | |||

5.95 | 5.92 | |||||

17.84 | 17.5 | 8 | ||||

89/46 | 65/89 | 89/3 | 62/96 |

Man | Woman | Man | Woman | Man | Woman | |
---|---|---|---|---|---|---|

10.05 | 11.1 | 10.22 | 11.49 | |||

20.54 | 22.92 | 20.77 | 23.89 | |||

45.72 | 51 | 47.1 | 49.01 | 1 | ||

01:49.6 | l:58.43 | 01:46.8 | 01:52.6 | 8 | 1 | |

03:37.3 | 04:04.7 | 03:38.2 | 04:08.9 | |||

08:22.0 | 08:32.9 | |||||

13.51 | 12.78 | 12.52 | 13.1 | 1 | ||

49.43 | 54.38 | 49.31 | 53.79 | 8 | 8 | |

13:29.2 | 13:55.0 | |||||

27:46.4 | 29:03.1 | |||||

1:25:47 | 1:15:54 | 1 | ||||

3:51:15 | 3:26:39 | 1 | ||||

2:15:00 | 02:28.1 | 2:15:73 | 02:17.9 | 1 | ||

20.14 | 18.06 | 20.35 | 18.75 | 8 | 8 | |

63.34 | 60.97 | 65.77 | 66.41 | 8 | 3 | |

85.76 | 62.52 | 80.78 | 58.83 | |||

77.13 | 69.72 | |||||

2.28 | 1.95 | 2.29 | 1.96 | 8 | 8 | |

8.27 | 6.74 | 7.98 | 6.51 | |||

5.78 | 5.57 | |||||

17.04 | 17.14 | 8 | ||||

82/99 | 62/00 | 81/18 | 61/84 |

According to the results of the gray prediction, at least 9 Chinese men's track and field events will enter the top 8 of the Olympic Games in 2021. Among them, 110 m hurdles, 20 km race walking, and 50 km race walking are expected to win medals in track and field. Projects like high jump and triple jump should continue to be developed as key projects. This can expand and maintain China's advantage at the world's track and field level [6]. And events like sprinting, long-distance running, throwing, and decathlon are still far from the world level. According to the gray prediction results, in 2021, at least seven Chinese women's track and field performances will enter the top 8 of the Olympic Games. Projects include marathon 400 m, 800 m, discus, shot put, high jump, and 400 m hurdles. Due to the late launch of the hammer throw, 20 km race walking, pole vault, triple jump, 5000 m, and 10000 m, it is not within the forecast. The marathon, 400 m, 800 m, and discus are among the items competing for medals. Shot put, high jump, and 400 hurdles are expected to be the top 8 items. The results of 100 m, 100 m hurdles, 200 m, 1500 m, javelin, long jump, and heptathlon are far from the world level [7]. Although the 20 km race walking, 5000 m, and 10000 m are not within the expected range, they can enter the top 8 according to the results of the previous Olympic Games. Even the hope of winning a medal is great.

The so-called nationwide system specifically refers to the guiding ideology, training management methods, and network system implemented in the field of competitive sports in China. The Chinese government attaches great importance to the strategic policy of the Olympic Games, while some coaches and athletes attach great importance to the strategic policy of the National Games [8]. From the rank-sum ratio of the individual best results of men and women in Chinese track and field from 1999 to 2005, we can see the best results in 2004 and 2005, namely the Olympic year and the National Games year. The ratio is 2:7 for men and 1:3 for women. At present, the population of China participating in basic track and field training does not exceed 100,000, and the population participating in systematic training is <100,000. A total of 52 athletes participated in the 2004 Olympic Games. Therefore, the jobs of most coaches and athletes are maintained in the National Games. If the National Games system is not resolved, it will affect the results of the Olympic Games.

Insufficient investment and difficulty in financing. Many necessary measures to improve the level of sports cannot be implemented in training competitions. Track and field events are more one-way (46 items), the team is large. Still, the level of exercise is relatively low, the social influence is low, and the attraction to enterprises is small, so it is more difficult to obtain social sponsorship. The insufficient investment makes track and field events, and although they are basic projects, they cannot be fully supported and developed [9]. Although we can make a difference in some projects, we cannot fully guarantee various teaching training methods in training and competitions. This is another reason why China's track and field performance is not high.

Scientific theoretical knowledge and technical methods are widely used in various fields of sports. Various new materials provided by material science are widely used in sports equipment, clothing, construction, and other utensils. Electronic computers, televisions, video recordings, and other audio-visual equipment directly lead people to the process of physical education and sports training as a means of education and training [10]. Various scientific research tools such as scientific research experiment equipment and testing tools are adopted by sports science research. Physiology, biology, biomechanics, biochemistry, psychology, and other disciplines have more deeply involved in the research and guidance of track and field sports from more aspects. These technologies increasingly play a role in improving technology, improving physiological functions, performing psychological adjustment, preventing and curing trauma, and selecting athletes.

Coaches play a leading role in sports training, and they are directly related to the improvement of scientific training levels and sports levels. The textbook ‘Sports Training Management’ proposes that coaches have moral character, knowledge quality, ability quality, conceptual quality, temperament quality, and physical quality [11]. After the mid-1990s, the Track and Field Sports Management Center of the State Sports General Administration was established. We have changed the training management system from the ‘centralized system’ to a ‘federal system.’ This has achieved certain results, but it also exposed many problems. Some coaches’ training plans, methods, and methods are kept secret, and even the phenomenon of mutual suspicion and unhealthy competition has arisen.

The competitive ability of track and field athletes refers to the ability of athletes to perform the highest exceptional results or defeat opponents in track and field competitions. In major competitions, the normal performance level of outstanding foreign athletes reaches about 60%, while that of outstanding Chinese athletes is only about 25%. In the 28th Olympic Games, 27.1% of Chinese track and field athletes performed normally, and <7% showed the highest level. 19.23% of the athletes performed well [12]. The level of 53.84% of athletes dropped more. This is significantly lower than the comprehensive international ratio.

Sports life refers to the period from good performance to the best performance for athletes until retirement. Chinese men's best results are between 20 years old and 26 years old, and women are between 18 years old and 24 years old. Compared with the best athletes globally, the best competitive age is <5 years old [13]. The entire sports life span is 8–10 years short, and the best competitive age is between 25 years old and 29 years old. They stay in the competitive age group for 8–10 years. The best competitive age range of Chinese elite track and field athletes is between 20 years old and 24 years old, and the length of the competitive age group is relatively short. Generally, 4–5 years, and the entire sports life span is relatively short.

The training management of grassroots sports schools deviates from the development stage of sports training. The selection of Chinese competitive sports consists of a three-level training system. The prefecture-level sports school manages the sports training process. The specific method is to link the various treatments of the coaches with the achievements of the athletes he trains. This ignores the physical and psychological development stages of children and adolescents. The evaluation system that only seeks results but not process leads to adultizing the training methods of children and adolescent athletes.

According to the results of gray prediction, focus on the development of sports that may enter the top 8 of the 2021 Olympic Games. Coaches and athletes should adjust their training plans from the National Games cycle to the Olympic cycle. We should adopt related policies to enable social organizations or individuals to increase their economic investment in track and field sports. Hire foreign coaches to coach and increase the training of excellent coaches. The coaches of the same project should communicate with each other. Improve the coaching level of the coaching team in terms of theory and practice. Pay attention to the training of mental training methods and sports psychology for athletes. Especially before the game, it is necessary to strengthen the training of mental preparation and sports psychology. Improve China's track and field training system. To extend the life span of Chinese track and field athletes, the best competitive age appears between 25 years old and 29 years old. This will ensure the sustained and stable development of China's track and field sports.

We predict that at least nine Chinese men's track and field events will enter the top 8 of the Olympic Games in China's track and field performance in the 2021 Olympic Games. Among them, 110 m hurdles, 20 km race walking, and 50km race walking are expected to win medals in track and field. At least seven Chinese women's track and field performances have entered the top 8 of the Olympic Games. The events include a marathon, 400 m, 800 m, discus, shot put, high jump, and 400 m hurdles. Factors affecting China's track and field sports development include the national system, economic investment, technological level, coaches, athletes, and training systems.

#### 2021 Chinese Men's and Women's No. 1 and Olympic Games No. 1, 3, 8 Predictions

Man | Woman | Man | Woman | Man | Woman | |
---|---|---|---|---|---|---|

9.87 | 11.01 | 9.98 | 11.26 | |||

19.84 | 22.27 | 20.03 | 21.28 | |||

43.92 | 49.39 | 44.73 | 49.67 | 1 | ||

01:44.9 | 01:56.7 | 01:44.9 | 01:56.8 | 8 | 1 | |

03:32.6 | 03:55.6 | 03:32.8 | 04:08.8 | |||

08:13.7 | 08:14.4 | |||||

110 mH | 12.91 | 12.52 | 13.13 | 12.59 | 1 | |

44.95 | 52.74 | 48.3 | 53.3 | 8 | 8 | |

13:24.9 | 13:24.4 | |||||

27:01.4 | 27:11.8 | |||||

0.0433565 | 01:20.4 | 1 | ||||

3:40:23 | 3:49:36 | 1 | ||||

2:10:52 | .2:24.36 | 2:12:09 | 2:26:24 | 1 | ||

20.75 | 19.11 | 20.71 | 18.84 | 8 | 8 | |

68.76 | 67.46 | 67.23 | 64.15 | 8 | 3 | |

89.22 | 68.53 | 87.96 | 63.93 | |||

80.402 | 78.61 | |||||

2.36 | 2.05 | 2.32 | 2.02 | 8 | 8 | |

8.49 | 6.95 | 8.32 | 6.9 | |||

5.95 | 5.92 | |||||

17.84 | 17.5 | 8 | ||||

89/46 | 65/89 | 89/3 | 62/96 |

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