Volumen 7 (2022): Heft 1 (January 2022)

In this paper, the main biological aspects of infectious diseases and their mathematical translation for modeling their transmission dynamics are revised. In particular, some heterogeneity factors which could influence the fitting of the model to reality are pointed out. Mathematical tools and methods needed to qualitatively analyze deterministic continuous-time models, formulated by ordinary differential equations, are also introduced, while its discrete-time counterparts are properly referenced. In addition, some simulation techniques to validate a mathematical model and to estimate the model parameters are shown. Finally, we present some control strategies usually considered to prevent epidemic outbreaks and their implementation in the model.

Using Python language and combined with data analysis and mining technology, the authors capture and clean the housing source data of second-hand houses in Chengdu from Beike Network, and visually analyse the cleaned data. Then, a Random Forest (RF) model is established for 38,363 data elements. According to the visual analysis results, the model variables are revalued, the key factors affecting house prices are studied and the optimised model is used to predict house prices. The experiment shows that the deviation between the house price predicted by the RF model and that predicted by the real house price is small; it also indicates the accuracy of the RF model and demonstrates its good application value.

According to the water characteristics of the coastal waters of Hebei Province, this paper selects the data of the Marine Environmental Quality Bulletin of Hebei Province from 2009 to 2018 published on the website of the Department of Natural Resources of Hebei Province, and proposes a red tide monitoring method based on decision tree classification for the pre-processed MODIS 1B image data. The most important thing in the construction of decision tree is the determination of threshold, and this process is finally determined according to the value of Entropy. In this paper, the newly constructed red tide monitoring method is used to extract the occurrence area of red tide and count the red tide area. Finally, the decision tree classification method is compared with other typical red tide monitoring methods. The experimental results show that the red tide occurrence area and statistical area extracted by the red tide monitoring method based on decision tree classification are closer to the data displayed in the Ocean Bulletin, which demonstrates that this method is suitable for red tide monitoring in the coastal waters of Hebei Province.

The latest “Guide to College English Teaching” lists cross-cultural education as an important part of college English courses. At the same time, ICAO ’s requirements for civil aviation pilots and controllers ’cross-cultural abilities increase year by year, which raises new requirements for the cultivation of cultural abilities. This article explores this subject from two aspects of cross-cultural psychology and cross-cultural behavior, using SPSS22.0 data analysis method and Delphi method to establish an evaluation model, which includes four first-level indicators: attitude, awareness, knowledge and skill. Attitude and consciousness evaluate cross-cultural psychology, and knowledge and skills evaluate cross-cultural behavior. Under the 4 first-level indicators, there are 6 second-level indicators and 17 third-level indicators. This paper uses the accuracy and convenience of language operators in the process of information conversion to transform fuzzy subjective qualitative analysis into quantitative analysis, and proposes a set of evaluation methods for cross-cultural competence based on language operators. At the same time, an empirical study was conducted with C University as an example. The statistical results show that the method has good applicability and scientificity for the evaluation of the cross-cultural competence of civil aviation college students.

This work introduces the foundation of a new class of input shaping algorithm, designed based on the particle swarm optimisation. This algorithm is utilised to control the residual vibrations in the crane system. The motivation is the development of simple algorithms and architecture for controlling the motion in under-actuated nonlinear systems with minimal modelling effort. By recording the payload swing signal of the crane only once, the approach can automatically calculate the optimisation amplitude and time locations of the impulses required by a common zero-vibration-derivative (ZVD) technique. In this work, we use this algorithm to design a ZVD shaper for controlling the motion of an under-actuated nonlinear crane model system. We validate the approach using experiments. If this algorithm is implanted into the embedded system and applied to the actual crane, which will solve the problem of the traditional ZVD parameter adjustment and improve the vibration suppression effect of the ZVD Algorithm.

To ensure the stability of the communication architecture in the power monitoring system, we propose an intelligent grid cyber-physical communication architecture modelling method based on the correlation characteristic matrix model. The article connects the physical entity layer, the information physical coupling layer, and the information system layer through an incidence matrix to form a complete power information physical system unit model. Through this system, we call the link and each node on the call link as the monitoring object, collect the relevant index data, and establish the business alarm mapping model of the communication network failure. The experimental results verify the reliability of the system and algorithm.

The power generation of distributed power generation systems in regional power grids is mainly affected by external environmental factors, and there are volatility and intermittent power generation issues. This paper establishes a relatively simple multiple linear regression prediction model to predict grid-connected photovoltaic power generation systems. The article uses a hybrid modelling method to filter more important weather forecast input variables through a step-by-step linear regression method to realize the visual calculation of power data. The research results show that the multiple linear regression equation methods proposed in the article have pervasive application value in the actual application of solar photovoltaic power consumption data.

This article proposes a nameplate recognition method based on the least-squares method and deep learning algorithm character feature fusion. This method extracts the histogram of the edge direction of the character and constructs the histogram feature vector based on the wavelet transform deep learning algorithm. We use classifier training for the text recognition of the nameplate to segment the text into individual characters. Then, we extract the character features to build a template. Experiments prove that the algorithm meets the practical application needs of nameplate identification of power equipment and achieves the design goals.

Computer vision technology and video image processing technology in the visual rehearsal of sports dance is a hot research topic. Based on this research background, the thesis uses 3D mathematical modelling technology to interpolate and extract the captured sports and dance movement information to make the final synthesised human animation natural, smooth and lifelike. At the same time, the thesis realises the method of action cohesion through the definition of characteristic action unit attributes and association constraints. Then, it applies it to the visual rehearsal system of sports dance. Finally, the analysis of experimental results proves that the proposed method can improve the precision and recall of rehearsal.

Carbohydrate metabolism can provide energy for human exercise. However, different exercise intensities will consume different amounts of energy. For this reason, the paper uses a fractional linear regression equation to study the characteristics of carbohydrate metabolism and energy consumption of other groups of human beings with the same oxygen consumption during exercise. In addition, the thesis measures energy consumption during exercise and body recovery by analyzing gas metabolism methods. As a result, we found that the sugar, fat metabolism, and energy consumption of heavier volunteers under the same exercise intensity were lower than those of regular weight volunteers. Thus, the fractional linear regression method can help us analyze the relationship between glucose metabolism and exercise energy.

This article uses the calculus method and three-dimensional analysis system to photograph and analyse the action techniques of China's famous basketball players’ shooting training. Combining with the action technical parameters of outstanding male basketball players at home and abroad, this article analyses several main basketball players’ shooting training actions. Quantitative analysis of the calculus method was carried out in the technical link, and the problems existing in the basketball player's movement technology were found. Further, from the comparison of the physical fitness of excellent athletes, the reasons for the gap between the level of basketball in China and the world were discovered, and the physical quality of excellent male basketball players was established. Level evaluation models and standards provide a reliable guarantee for accurately grasping the development of athletes’ physical fitness, clarifying the status of each physical fitness in training, optimally controlling the basketball training process, and achieving scientific basketball training.

Based on the factors affecting sports performance, from a more comprehensive and broad perspective, after consulting the literature, 52 factors that affect the outcome of football matches are selected, including technology, tactics, physical fitness and referees’ penalties. By watching the video of the game, 52 influencing factors of 200 games and 400 teams were counted. The original data was statistically processed with correlation analysis and multiple linear regression analysis, and the statistics of the 26 European Cup games were substituted into the winning formula. To verify the scientific nature and objectivity of the formula, we aim to ascertain the core factors in the winning factors of a football game and the quantitative relationship between these factors and the result of the game, so as to provide a certain reference for football training, game analysis and scientific research. The technical and tactical ability of individuals and teams is the core competitive ability factor that affects the result of the game; from a single factor, 15 factor indicators have a significant impact on the result of a football match; on the whole, 10 factor indicators have a significant effect on the result of a football match. In addition, there is a certain quantitative relationship between these influencing factors and the results of the game; empirical evidence shows that the football game winning formula has a certain degree of science and objectivity.

The discretization of fractional-order differential operators is the key to the digital realization of fractional-order controllers. This paper proposes an improved second-order fractional differential equation operation method based on power series expansion. The algorithm's operation speed and accuracy performance are analyzed. The research found that the algorithm proposed in this paper is suitable for the fractional operation of arbitrary signals, including discrete data sequences whose mathematical model is unknown and the solution of linear systems.

Due to the extremely volatile nature of financial markets, it is commonly accepted that stock price prediction is a task filled with challenges. However, in order to make profits or understand the essence of equity market, numerous market participants or researchers try to forecast stock prices using various statistical, econometric or even neural network models. In this work, we survey and compare the predictive power of five neural network models, namely, back propagation (BP) neural network, radial basis function neural network, general regression neural network, support vector machine regression (SVMR) and least squares support vector machine regression. We apply the five models to make price predictions for three individual stocks, namely, Bank of China, Vanke A and Guizhou Maotai. Adopting mean square error and average absolute percentage error as criteria, we find that BP neural network consistently and robustly outperforms the other four models. Then some theoretical and practical implications have been discussed.

With the intensification of social competition, the rate of return to education is gradually decreasing. This leads to a reduction in the indirect effect of education on happiness. This article uses the bivariate ordered Probit model under the educational field theory to investigate the impact of higher education innovation on social class and residents’ happiness. The results show that the innovation and reform of higher education will have a certain impact on residents’ happiness. The improvement of education level can significantly improve the individual's subjective well-being, and there are significant urban-rural differences. This shows that education reform and innovation are imperative.

The digital and physical methods of establishing minimal curved surfaces are the basis for realizing the design of the minimal curved surface modeling structure. Based on this research background, the paper showed an artistic surface modeling method based on nonlinear over-limit difference equations. The article combines parameter optimization and 3D modeling methods to model the constructed surface modeling. The research found that the nonlinear out-of-limit difference equation proposed in the paper is more accurate than the standard fractional differential equation algorithm. For this reason, the method can be extended and applied to the design of artistic surface modeling.

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.

As a subsidiary institution of collecting and preserving cultural relics, human cultural heritages and developing information resources, museums are important places to display, disseminate and study excellent national cultures. With the development of the economy and the improvement of people's living standards, people's demand for spiritual culture is getting higher and higher, and museums are getting more and more attention from people. Thanks to the rapid development of computer technology, more and more museums are focusing on informatisation. This article will use the information system's functional mapping method based on the museum's improvement and test analysis, which can make the museum's business unit with the use of the unified system platform, under a unified, homogeneous standard data for the orderly organisation of information resources sharing and efficient, rapid building of information resources of lateral connection, make the administrative, business interaction and interrelated information collection with Word Perfect data integration, and create a museum management platform more conducive to innovative thinking. The innovation system mechanism, to improve the way of ZhanChen for the museum, to speed up the informatisation construction museum, make a museum of play to better spread knowledge, transfer civilisation, materialisation of education function and the important window displaying the world the outstanding civilisation achievement effect, and promote the development of cultural undertakings, where science has a very important realistic and far-reaching historical significance.

Differential equation modelling was earlier used to discover better and understand various biological phenomena and social problems. We hope to understand the stability of the system and the Hopf bifurcation based on the characteristic roots of the linear system. Because group competitive sports require participants to have certain competitive skills, those who do not have sports skills but want to develop into activities must receive training and specific training. Therefore, based on the research background, the article proposes a time-lag group competitive martial arts activity model with a time lag effect. Through delay differential equation theory and Hopf bifurcation theory, the stability of the equilibrium point and the existence of periodic solutions generated by the Hopf bifurcation caused by the ‘instability’ of the equilibrium point are discussed. Finally, the theoretical results are simulated and verified with the help of MATLAB software.

In the continuous application and development of network technology, the reform in Internet information will inevitably bring about major changes in college education and teaching. Based on this background, the paper puts forward the influence of ‘Internet+’ on art design education. At the same time, the article explores the influence factors of the Internet on art design teaching based on the non-linear equation model. We use the parameterised cubic clipping algorithm to find the roots of non-polynomial equations. Through performance analysis and comparison, it is found that the root-finding algorithm proposed by us has better parallelism and lower-storage requirements. This algorithm has certain advantages in solving the weight of the factors that influence the Internet to art design teaching.

With the rapid development of the world economy, some developing countries only pay attention to the growth rate of GDP, but ignore the importance of sustainable development. The extensive economy, which relies on a lot of energy to drive economic growth, can no longer meet the development requirements of a low-carbon economy. Fundamentally changing this mode of economic growth, optimising the energy structure will become an effective key path. This paper starts with the current situation of the government's development of a low-carbon economy, and analyses the factors affecting it. In order to develop a low-carbon economy, reducing haze pollution and greenhouse gas emissions, energy conservation and emission reduction work of the logistics industry becomes imminent. To analyse the current situation of logistics energy efficiency and structure, qualitative and quantitative research methods are used to measure the impact of these indicators on a low-carbon economy, predict the total energy demand and supply under different scenarios, and formulate the best scenario to optimise the energy structure. Finally, the government put forward the grey prediction management scheme for the development of a low-carbon economy.

This article summarises 15 factors that affect the collaborative innovation of industry, university and research through literature research and establishes the innovation entity and innovation environment subsystem of the collaborative innovation system of colleges and universities based on the theory of synergy. By setting system boundaries and causal relationship analysis, the dynamic model of the collaborative innovation system in colleges and universities is established, and the model's validity is verified. Combining the actual work, the enlightenment of collaborative innovation management in colleges and universities is as follows: Develop collaborative innovation led by scientific and technological talents strategy. Strengthen the policy and system support for collaborative innovation of colleges and universities. Improve the collaborative innovation input mechanism of institutions of higher learning.

To study the teaching of sports science in athletics, this paper adopts the method of a nonlinear mathematical equation, According to the explosive power = force * speed and hill force speed equation, the best matching value between the load weight and the muscle contraction speed when the athlete reaches the maximum explosive power is obtained by the mathematical method, to achieve the objective of quantifying and scientifying the maximum explosive power training method according to the individual ability of the athlete. The results show that the training intensity is slightly lower than the optimal strength load (about 30%F0) and faster than the optimal movement speed. Jumping events adopt load weight higher than the optimal load to 50% F0 and load intensity slightly slower than the optimal speed combination for training; Conclusion: According to the characteristics of track and field events, this paper discusses the application of the research results in the training of athletes’ explosive development in different track and field events, to achieve better training effect and improve students’ athletic ability.

The analysis and structural transformation of power-related picture elements is an essential result of regional power grid research. This paper proposes a new idea for extracting monolithic insulator images based on analysing the characteristics of scanned colour grid power insulators. At the same time, the article extracts the RGB colour matrix of the insulator based on the BP neural network algorithm. Then, it uses it as a characteristic parameter for training and analysis. Combining the characteristics of image data, it is found that the model proposed in this paper enhances the ability to express images, thereby improving the accuracy of image classification. Furthermore, many experiments on the accurate data set of insulator monoliths show the effectiveness of this model.

The article uses SPSS statistical analysis software to establish a multiple linear regression model of short-term stock price changes of domestic agricultural listed companies. The article uses a stable time series based on the ARMA model for stable agricultural value-added, fiscal expenditure and market interest rates. The regression method is used to study its impact on the stock price index. Compared with the existing stock forecasting methods, this method has simple data collection and no specific requirements for data selection, and the prediction results have a high degree of fit. Therefore, this method is suitable for most stocks.

This article combines geographic information system (GIS) technology and database technology to analyse agricultural, natural disasters. The article uses a fractional linear regression equation to define the comprehensive intensity grading standard of the disaster-causing factors of torrential rain. At the same time, we use GIS to superimpose the agricultural vulnerability index into the storm disaster risk zoning to obtain the degree of agricultural impact under different levels of risk. At the end of the thesis, the model is applied to actual case analysis to verify the effectiveness of the algorithm model.

The article analyzes why colleges and universities should strengthen innovation and entrepreneurship education based on “mass entrepreneurship and innovation”’ First, we conduct a questionnaire survey on the status of college students’ innovation and entrepreneurship attitude and use nonlinear methods to construct an evaluation model of innovation and entrepreneurship capabilities to evaluate students’ innovation and entrepreneurship capabilities quantitatively. Finally, we verify the effectiveness of the combined evaluation model through data on the innovation and entrepreneurship activities of college students. The research results can provide a new idea for appraisal of college students’ innovation and entrepreneurship ability.

As the pace of national modernisation accelerates, the society urgently needs talents with entrepreneurial qualities and innovative spirit. Therefore, colleges and universities need to vigorously cultivate the entrepreneurial quality and innovative spirit of college students. We believe that the quality evaluation index system for implementing innovation and entrepreneurship education should be constructed from the perspectives of university students, colleges and universities and the external environment. The article constructs a structural equation model (SEM) with seven hidden variables and 23 observed variables. By revising the hypothetical model, it is concluded that the total effect of cultivating innovative and entrepreneurial talents is 0.48. Therefore, we believe that the current development of postgraduate innovation and entrepreneurship education is still very unsatisfactory. The entrepreneurial situation of students has not attracted the attention of colleges and universities. The allocation of resources, full-time teachers and the curriculum system need to be further improved.

After a lot of literature reading and practical research, the paper uses the parametric modelling method of curve simulation characteristic line to establish the mathematical model of the furniture product leg shape. This article first uses the surface construction method to analyse the composition of the leg size of the industrialised production and manufacture of furniture products, and makes the solid modelling according to the construction method of non-uniform rational spline mathematical curve and surface simulation. At the same time, the parameter function of furniture leg type is set on SolidWorks, and the research results obtained in the paper are found by simulation, which opens up a new research path for the application of mathematical curve model in furniture design.

This article proposes a distribution function based on normal distribution to express the distribution of criterion values in the interval. This method considers that the economic evaluation target of investment projects is multi-attribute. The economic management risk control environment is divided into information environment, time and space environment, and subject environment. The paper gives the corresponding multi-attribute economic evaluation method for the six possible combinations of project risk environments under the possibility of mutual comparison between interval numbers under the normal distribution. In the end, an example is used to illustrate the practicability and simplicity of the decision-making method.

In physical education class, the movement of the human body requires multiple joints to cooperate, and a multi-link system coupling is presented. In the teaching of physical education curriculum, the impact of the force received by students jumping up and down shows the characteristics of the non-linear system of physics and mathematics. Aiming at the movement process of jumping up and down, we established a joint mathematical equation model of the motion state of the human lower limb joints. We use a non-linear system to solve the mathematical model of the joint force coupling problem of the human body jumping up and down.

The paper derives the current-voltage relationship in the semiconductor circuit breaker based on the equation of fluid mechanics which has application for safe and water access. Then, the paper proposes a Newton iterative method based on the finite element analysis method to solve the nonlinear algebraic equation relationship in the semiconductor circuit breaker. At the same time, the paper constructed a coupled numerical model based on the hydrodynamic equations and applied it to the pulse current prediction. Experiments have proved that the algorithm can realize large-scale open-circuit switching current forecast, and the algorithm has high efficiency and accuracy.

This article first introduces neural networks and their characteristics. Based on a comparison of the structure and function of biological neurons and artificial neurons, it focuses on the structure, classification, activation rules, and learning rules of neural network models. Based on the existing literature, this article adds a distributed time lag term of the neural network system. In the actual problem, history has a very important influence on the current change situation, and it is not only at a specific time in the past. It has an impact on the current state change rate. Therefore, based on the existing literature that only has discrete time lags, this paper adds distributed time lags. Such neural network systems can better reflect real-world problems. In this paper, we use three different inequality scaling methods to study the existence, uniqueness, and global asymptotic stability of a class of neural network systems with mixed delays and uncertain parameters. First, using the principle of homeomorphism, a new upper-norm norm is introduced for the correlation matrix of the neural network, and enough conditions for the existence of unique equilibrium points in several neural network systems are given. Under these conditions, the appropriate Lyapunov is used. Krasovskii functional, we prove that the equilibrium point of the neural network system is globally robust and stable. Numerical experiments show that the stability conditions of the neural network system we obtained are feasible, and the conservativeness of the stability conditions of the neural network system is reduced. Finally, some applications and problems of neural network models in psychology are briefly discussed.

The thesis applies solutions to boundary value problems of a class of fractional differential equation coupled systems with a p-Laplacian operator. This article applies this part of the content to alleviate the psychological barriers of college students. This article transforms the tendency of individual consciousness in college students’ psychological counselling into a problem of solving boundary value problems of fractional differential equations. Studies have shown that using fractional differential equations to analyse the causes of college students’ psychological barriers has an essential role in eliminating college students’ psychological barriers.

The angle steel-concrete column used in the new frame structure means that the rigid angle steel is placed in the column instead of the longitudinal reinforcement. The steel plate hoop welded to the longitudinal angle steel is used instead of the stirrup to form a spatial steel frame and concrete component. To ensure the normal use of existing houses in the building and adding floors, avoid transferring the load during the construction phase to the roof of the original house. The corresponding skeleton curve is extracted from the hysteresis curve of the specimen. Based on experimental research, the force performance of the normal section of the angle steel-concrete column was discussed, and the calculation formula of the normal section bearing capacity of the angle steel-concrete column was discussed.

Water is a key factor that controls the evolution of the ecosystem and restricts social and economic development. The rational allocation of water resources is the basis for the basin's sustainable use of water resources. The article uses fractional differential equations to discuss the increasingly prominent contradictions between supply and demand of agricultural water resources, serious pollution and overexploitation, the decline in groundwater level and water quality, low agricultural water efficiency, and serious waste from the perspective of sustainable development. Second, the article classifies the index system of the water resources carrying capacity evaluation model. Finally, model the resource balance of water supply and water demand in the irrigation area. The study found that the water quantity analysis and determination of the irrigation area will have important guiding significance for implementing the irrigation area's continued construction and water-saving transformation. The allocation and utilization of water resources in farmland irrigation areas will tend to be rationalized. This will greatly improve the water-saving efficiency of irrigation districts.

To systematically understand the ability and technical mastery of football training of ethnic college students in colleges and universities, we use fractional differential equations to analyze the passing technique of college ethnic football. Research has found that establishing differential equation models in football can help us use mathematical ideas, methods, and knowledge to solve practical problems.

This article proposes a mental health education model for college students based on non-linear finite element equations and explores the concepts, content, methods and approaches for mental health education. After analysing college students’ psychological behaviours, the study is based on stressors and stress response models. It specifically explores the psychological and behavioural manifestations of college students with four different attachment types. The research provides a preliminary theoretical basis for the mechanism of the psychological and physical health of college students.

College students are prone to psychological changes and personality distortions under heavy pressure. It will lead to catastrophe if it is not promptly guided or improperly used to reduce stress and relax. Now we integrate holistic education into the construction of the mental health education system in colleges and universities. This is conducive to solving practical problems and improving the effectiveness of system construction. We set up a differential equation model (DCE) based on the discrete choice to study mental health due to practice. At the same time, we adopt the mutual influence model of penetrating dissemination of thoughts and public opinion and human behaviour, and establish the SEIR DCE with constant input and bilinear incidence rate. The experiment verifies the algorithm’s effectiveness on the model of whole-person mental health education activities in colleges and universities.

To realise the optimisation of Building Information Modelling (BIM) technical engineering project management, the paper conducts data investigation and analysis of the technical problem which deals with a specific power grid tunnel construction. This article uses BIM to sample considerable data information for the construction and management of power grid tunnels. According to the geological factors of rock strength in construction, the fuzzy information fusion method is used to carry out the feature fusion and adaptive scheduling of management information. We will extract the characteristics of each surrounding rock category's geological BIM information association rules and use the multiple regression analysis methods to carry out the BIM information fusion and adaptive scheduling of the tunnel construction project management. The study results confirm the conclusion that the predicted scores are in good agreement with the geological scores on site.

User consumption behaviour is a subject worthy of study. Because consumers’ consumption behaviours are dynamic and with individual differences, various factors need to be considered when establishing a fractional differential equation model of users’ online consumption behaviour. The two elements, namely advertising and price are more evident in influencing consumer behaviour. Therefore, the paper establishes a product diffusion fractional differential equation model of price and advertising presence or absence to study the impact of these two factors on consumer behaviour. It turns out that ignoring the advertisement and the cost of the product is related to the characteristics of the consumer network. When there are advertising and price factors, product awareness is related to price constraints.

To study the landing point of the curved football track, the dynamic differential equations of the football were derived in this paper. The air resistance moment was taken into account, and the rotation axis was no longer confined to the vertical direction. We compare various soccer movement regularity of different initial angular velocity 0, in turn, using standard numerical methods to solve differential equations, the selection of the initial angular velocity of three typical 0s has been carried on the detailed numerical study, and the results show that: in the same velocity V play football, corresponding to different initial angular velocity 0, the movement of football is an obvious difference. Conclusion: For the same V = 5 + 28 + 11 m/s, when no rotation Ω 0 = 0, the trajectory of the football is the usual trajectory of the projectile. When 0 = 2 − 2 + 16 rad/s, the trajectory of the football is a typical banana ball trajectory; When 0 = 13+0+0 rad/s, the trajectory of the football shows the phenomenon of left-right fluttering, similar to the fallen leaf ball.

In order to solve the problem that the image processing time is too long in the use of the original college education information power method, therefore, the design of the fractional differential equation of higher education information power method was created. According to the information source, a combination of various methods is set to complete the data collection. Compared with the content of fractional differential equation, the fractional differential equation is selected to complete the image information processing, develop the processing process and select the appropriate equipment to complete the image processing, set up the experimental equipment, and select the experimental samples to obtain the experimental results. Compared with the original method, the image processing time of this method is significantly shorter than that of the original method. Therefore, this method is more efficient for image processing and has a more obvious effect on the informatisation of university education.

College students continue to improve their consumption levels due to compassion or vanity, but it not only increases the financial burden of the family, but is also not conducive to their personal health. In order not to affect the mental health of college students, to solve the problem of mutual comparison consumption, this paper establishes differential equation models to describe this phenomenon, from qualitative and quantitative angles to interpret and predict the results of comparison consumption. The results show that the current consumption behaviour of college students also has a reasonable place for being unreasonable, mainly from college students’ own and living environment.

To help people solve unsolved problems in everyday life and solve the complexity of life, this paper proposes an artificial intelligence algorithm and establishes a mathematical model for simulation experiments. The results show that the artificial intelligence algorithm can search the optimal solution in a short time, with a success rate of 95.87%. Under the same conditions, relative to other algorithms, it can not only improve the success rate of the optimal solution, but also the search solution has very significant advantages.

In order to meet the social demand for preschool education professionals, based on the finite element higher-order fractional differential equation, this paper studies the information teaching model of preschool education of fine arts in colleges and universities. Through the scientific and effective fine arts education in the preschool education major in colleges and universities, the students’ fine arts ability can be effectively improved, and the application of information means can make this goal can be better realised so that the teaching needs can be better satisfied and they promote the better development of fine arts education in the preschool education major.

In order to study the informationised teaching model of track and field education, this paper uses the finite element higher-order fractional differential equation to simulate, to provide high-quality, strong resistance to pressure, physical and mental health talents for the development of the country, through the study of the higher-order fraction of the finite element and track and field course intended to strengthen the application in the innovation of track and field course. The results show that based on the finite element theory of higher-order fractional differential equation, a new teaching model is constructed to solve the current difficulties faced by track and field. Starting from the teaching end, pay attention to the quality of output so as to achieve the purpose of training qualified personnel. Conclusion: In the course of track and field classroom practice based on finite element high-order fractional differential equation, students’ enthusiasm is mobilised, and they take the initiative to learn knowledge and master skills.

In order to solve the problem of the traditional gray prediction model (GM) during determination of the accuracy of buildings’ energy savings and its poor fitting of data, the idea of a fractional model based on the traditional first-order one-variable GM(1,1) model is applied. We use the GM–backpropagation (GM-BP) neural network to solve the optimal fractional order and establish a fractional GM(1,1) model based on the GM-BP neural network. Example calculation shows that the fractional GM(1,1) model can improve the prediction accuracy of buildings’ energy savings, and selecting the optimal order can further improve the prediction accuracy and decrease the error level when using the GM-BP neural network. This work shows that the fractional GM(1,1) model based on the GM-BP neural network has an important guiding role in the energy savings of buildings.

In order to improve the detection and filtering ability for financial data, a data-filtering method based on mathematical probability statistical model, a descriptive statistical analysis model of big data filtering, probability density characteristic statistical design data filtering analysis combined with fuzzy mathematical reasoning, regression analysis according to probability density of financial data distribution, and threshold test and threshold judgment are conducted to realize data filtering. The test results show that the big data filtering and the reliability and convergence of the mathematical model are optimal.

Mental health is an important basic condition for the adult development of college students, and education workers gradually pay attention to the strengthening of mental health education for college students. In this paper, a psychological management system based on the K-means clustering analysis method is proposed. Based on the basic functions of the traditional system, the students’ psychological data are reutilised by using the idea of data mining. By optimising the iterative process of the K-means algorithm, the valuable parts of a large number of precipitation students’ psychological data are extracted. A data model is established and it provides decision guidance for managers to scientifically manage students’ mental health process. The system establishes the data mining model in the process of analysis, carries on the mining to the students’ psychological data in the database, analyses the different college students’ mental health state characteristics and provides the corresponding solution. The part of the test drew on mental health data from 1,000 students at a school, and the results show that the system uses the k-means algorithm to divide students into 3 categories, which are 20.6%, 31.9% and 47.1% respectively, which are 1.6% different from the data test results in the ideal state.

This paper takes the credit risk management of commercial banks in China as the mainline, and puts forward a quantitative model that is suitable for the credit risk management of commercial banks in China at present – Logistic regression model, and takes a commercial bank as an example, using the regression model to conduct empirical research on the credit risk of enterprises. The estimated Logistic model was tested with confirmation samples. The results show that when the cut-off point is set to 0.5, the overall correct rate of the model for the credit risk measurement of natural persons and for enterprises reaches 84.9% and 88%, respectively. When the cut-off point is set at 0.7, the overall accuracy is 89.2%. In general, the results of credit risk measurement of bank customers by the Logistic model are quite satisfactory. The Logistic Regression model is easy to understand and efficient, so it is worth popularising and putting into practice in commercial banks in China.

In order to establish a more accurate Stock Price Prediction Model, the Stock Price Prediction mathematical Model SPPM (Stock Price Prediction Model) based on BP neural network with high frequency data is proposed in this paper. The SPPM integrates several neural networks to predict the movement of stock prices over the next few days. The key problems in SPPM—such as data preprocessing, output fusion and the selection of nodes in the hidden layer of neural network—are discussed in detail. The experimental results show that the SPPM predicted the closing price of 2019-03-19 and 2019-03-20 as 207.16 and 207.22, respectively, which is very close to the actual observed value, and the back propagation mathematical model SPPM has a certain practical value. Our conclusion is that the back propagation model can predict the stock price with high accuracy.

In order to improve the information quality of financial accounting reports, this paper puts forward a functional differential equation, establishes the determination model of fair value by mathematical analysis method and studies the correlation of financial accounting information of fair value through this model. The results show that according to the fair value determination model, in the free accounting environment, fair value financial accounting information has an impact.

In order to solve the problems of financial accounting measurement quickly and accurately, this paper starts the analysis from the perspective of mathematics and finance and establishes the differential equation and the generalised functional equation for the related numerical analysis through mathematical knowledge. The results show that the limit and integral of rigid differential equation and the rigid generalised functional equation can improve their role and status in the financial accounting measurement environment so that they can be more widely used in the financial accounting measurement environment and promote the development of the financial accounting environment.

To reflect the country's economic growth, inflation and the implementation of monetary policies. Based on the monthly data of national debt yield from January 2015 to December 2019, these data are divided into 1 year to 30 years according to the maturity period, and the principal component analysis of the term structure of interest rate from 2012 to 2017 shows that the factors affecting the change of term structure of interest rate include level factor, skew factor and curve factor. The variance contribution rates of these factors to the variation of interest rate term structure curve are 82.2002%, 16.9948% and 0.6283% respectively. The horizontal factor represents the position of the term structure of interest rate, the skew factor represents the degree of skew of the term structure of interest rate, and the curve factor determines the interest rate.

Economic globalisation and the development of financial trade liberalisation lead to a higher probability of financial crises. At the same time, the occurrence of financial crises has a particular risk of contagion. Based on this research background, this paper constructs a dynamic Copula model. It demonstrates the application of this model in financial market risk management based on the correlation changes between the US stock market and the Chinese stock market before and after the financial crisis. The results show that the Standard & Poor’s Index and China before the crisis broke out There is a specific correlation between the stock markets, which shows that the financial crisis has affected both the Chinese and American stock markets. Therefore, risks in the financial market are contagious.

The characteristics of non-Gaussian clutter in radar systems are different from standard waveforms. To fully filter to achieve the accuracy of radar detection, the paper developed a radar simulation system based on virtual reality technology. The article uses a non-Gaussian mathematical model to simulate and collect the clutter generated by the system and realise the generation of data sequence according to the power spectrum. The research results show that the radar cross-section modelling, target recognition, anti-recognition and data fusion technology of visible targets can all be well applied in this system.

The thrust of basalt fibre (BFRP) tendons will result in narrower transverse crack spacing, decreased load transfer capacity of transverse cracks and voids at the bottom of the slab, which will lead to thrust failure. The thesis uses the finite element analysis method to analyse the material characteristics of BFRP tendons. At the same time, the article determines the critical load position corresponding to the tensile stress of concrete and BFRP tendons, and analyses the influence of voids, crack spacing and other factors on the load stress of concrete and BFRP tendons. The study results found that continuously reinforced concrete and asphalt overlay composite design can reduce cracks.

Risk transmission has three elements: risk source, risk flow and risk carrier. The paper quotes the asymmetric model and the joint asymmetric model to analyse the conduction effects of financial risks. At the same time, the article uses the elasticity coefficient to quantitatively calculate the risk transmission effect of the two supply chain financial financing modes. The research results prove that the risk transmission ability of each financial market has individual differences, and the foreign exchange market does not have significant risk transmission ability to other markets during the rising stage. The joint asymmetric model is more effective in predicting corporate financial risks.

The paper establishes a related differential equation model about changes in financial interest rates. It uses information related to liquidity to feedback the law and stability of differential equations in interest rate changes. The article applies stochastic processes and partial differential equations to complex financial networks to confirm node yields in financial market networks. It confirms the existence of interest rate stickiness in Chinese financial markets. The advantage of this interest rate model is that when the external economic environment changes, the state of interest rates will also change accordingly.

The paper establishes a related differential equation model about changes in financial interest rates. It uses information related to liquidity to feedback the law and stability of differential equations in interest rate changes. The article applies stochastic processes and partial differential equations to complex financial networks to confirm node yields in financial market networks. It confirms the existence of interest rate stickiness in Chinese financial markets. The advantage of this interest rate model is that when the external economic environment changes, the state of interest rates will also change accordingly.

China's tourism industry developed rapidly in the late 1990s, and its direct result is the continuous and rapid growth of tourism operating income. However, since 2010, China's tourism development has been slow and regional tourism development has been uneven. Even in different years in the same area, the tourism operating income shows great differences. How to select the key factor from many factors, as there is still no recognised method in the theoretical circle. This article combines the theories of econometrics, differential calculus, statistics and other related fields. Through in-depth basic research, the data required for the research is determined, and such data are substituted into the self-constructed econometric differential statistical model. Effective analysis of empirical objects is realised. At the same time, the article uses tourism operating income as an indicator and uses the analysis of variance method to calculate the average coefficient of variation of the same region in different years and different regions in the same year, analyses the trends and characteristics of China's tourism in the temporal and spatial structure, and proposes corresponding results on this basis.

After reviewing many literature foundations, the thesis combines the basic methods of elastic mechanics with mathematical knowledge, sets the bipotential stress potential complex function and analyses the relationship between stress component, strain component and stress potential function, and applies the complex variable function. The expression of the relevant stress component is derived, and the displacement boundary conditions of the surrounding rock of shallow circular tunnel are obtained. Furthermore, the paper applies the basic theory of complex variable function to solve the boundary condition complex variable function for common tunnel sections, and obtains the analytical expression of the surrounding rock stress of shallow circular tunnel. The simulation is carried out by finite element method. The establishment of complex variable function has a good application value in solving the stress of surrounding rock of shallow tunnel.

First, the research results of using game theory in the field of agricultural product quality and safety at home and abroad are reviewed and summarised, and the shortcomings of classical games theory are pointed out in most studies. The evolutionary game theory is used to explore the strategic space and evolution trend of agricultural product supply chain. Through the construction and analysis of a game model for the evolution of agricultural product quality and safety, the evolutionary phase diagram of the agricultural product supply chain market and evolutionary stability characteristics at each equilibrium point are obtained, which well reveal the evolutionary process of the agricultural product supply chain and effectively formulate related policies. Scientific basis for ensuring the quality and safety of agricultural products is provided.

Economic benefits continue to increase with the rapid development of the tourism industry. The level of tourism development is an indicator to measure the maturity of a country’s tourism industry. The article takes China’s coastal provinces as the research object and uses finite element ordinary differential mathematical equations to explore the income indicators of the tourism industry in coastal cities. In the dynamic process, the article portrays the development trend of tourism in different regions. It analyses the income levels and indicators of tourism development in coastal cities under different time and space conditions. The research results show that we can divide the time zone to count the base period value and average growth rate of domestic tourism in each province to classify the regional response type of domestic tourism development.

Commercial bank asset-liability management is a method of overall risk control and resource allocation. It has an essential impact on commercial banks’ operational safety and affects the stability of a country's overall financial system due to the domino effect. The article chooses the regression function model to measure the expected default frequency (EDF) in the resource allocation risk of Chinese banks. It analyses the transmission process of the impact of the main macroeconomic variables on the EDF of the resource allocation risk of Chinese commercial banks. The study found that under the significance level of 5%, standardised industrial output growth rate, money supply growth rate, and real estate price index are the main reasons for the changes in bank resource allocation risk EDF.

In order to study the fair value analysis of financial accounting, the Euler wavelet method is proposed to solve the numerical solutions of a class of Lane-Emden type differential equations with Dirichlet, Neumann and Neumann-Robin boundary conditions. The results show that the fractional integral formula of Euler wavelet function under the Riemann-Liouville fractional order definition and the L∞ and L2 errors of Haar wavelet are derived by the analytic form of Euler polynomial. By fixing M=4 and increasing the resolution scale k of Euler wavelet, a stable convergence solution can be obtained. The Lane-Emden equation with boundary conditions is transformed into algebraic equations by Euler wavelet collocation method, and the numerical results are compared with the results and exact solutions of other methods. The application advantages of fair value can be exerted through financial accounting to promote the transformation and upgrading of enterprises and realise the stable economic growth.

Basketball tactical scoring is a complex dynamic system with random changes. According to the principle of X fuzzy mathematics system analysis and comprehensive evaluation, the article uses a fuzzy comprehensive evaluation method to study the scoring of basketball tactics examination. The article calculates the weight coefficient of each index in this evaluation index system and provides adequate guidance for the training of basketball players.

Based on the shortcomings of the current intelligent management of distribution networks, the article designs and implements a remote intelligent detection system for live distribution networks. The article constructs and realises an algorithm based on a genetic algorithm (GA) and agent system. The algorithm is applied to energy-saving intelligent supervision of equipment in the distribution network. The simulation experiment shows that the integrated algorithm based on GA and agent system can accurately detect power quality in real time. At the same time, the algorithm can monitor the energy consumption of equipment in the distribution network under multiple disturbances.

Harsh environments such as alternating wet and dry conditions and cyclic loading cause erosion in steel bars, leading to severe damage to structures. Steel bars are also prone to bending under long-term fatigue loads. This paper establishes the bending performance test of corroded reinforced concrete (RC) beam under fatigue load based on the mathematical–statistical algorithm. It investigates the influence of heavy load on the fatigue performance of damaged RC beams, the influence of corrosive environment on the fatigue performance of RC beams, the degree of corrosion of steel bars in concrete beams under fatigue loading, and the distribution of chloride ions. The study results found that the stress ratio has a significant effect on the maximum crack width of the specimen beam. The greater is the stress ratio, the longer the fatigue life. This directly affects the performance of the specimen beam under fatigue loading. For this reason, we should pay special attention to the impact of corrosion on the fatigue performance of a structure during the design of steel bars.

This article conducts a dynamic simulation on new agricultural product networks’ psychological selection based on the evolutionary game theory. Aiming at the characteristics of fresh agricultural products, the article analyses the dynamic evolution process of consumers’ strategic choice psychological state in the model. The research results show that the new agricultural products platform and the seller's strategic choice for the quality of the product are closely related to the output ratio of the input to the quality of the product. The users of fresh agricultural products are organically related through various network information behaviours, forming a networking group with a particular topological structure relationship.

The financial system is a complex, nonlinear chaotic dynamic system caused by its operating mechanism. Therefore, the application of previous forecasting models cannot explain the existence of various interference factors in the financial market and the chaotic characteristics of the financial system. With the help of financial market stability, the article establishes a series of differential equation models that reflect changes in interest rates in the financial system. The article introduces the factor of macro-control on the premise of respecting market regulation to regulate and intervene in economic relations and economic operation status. We apply the Logistic model and stability theory to analyse the positive equilibrium point characteristics of the system and obtain the interest rate liquidity equation with a time-lag financial network.

Random multi-attribute decision-making is a finite option selection problem related to multiple attributes, and the attribute values are random variables. Its application and supply chain risk management can transform interval decision numbers and fuzzy decision numbers into standardised decisions. Based on this research background, the article provides a primary method to determine the randomness of standard random variables based on expectations and variance through theoretical analysis. Second, the article determines the range of the total utility value of each supply chain selection plan based on the 3σ principle. Experiments have proved that this method can solve unifying opinions due to different knowledge, experience, and preferences of evaluation experts. This provides a new method of supplier selection.

The advantage of the linear fractional differential equation for bank resource allocation and financial risk management is that it can test random fluctuations in different functional forms. Given this paper is modelling the asset allocation risk model for rural commercial banks, the linear fractional differential equation analysis method is used to make policy recommendations. The research results of this paper show that credit risk is significantly negatively correlated with the bank's resource allocation. The degree of negative correlation between different levels of credit risk and bank resource allocation is different. Appropriate liquidity risk can optimise the bank's resource allocation.

To reduce the probability of violent crimes, the deep learning (DL) technology and linear spatial autoregressive models (ARMs) are utilised to estimate the model parameters through different penalty functions. In addition, under a determinate space, the influences of environmental factors on violent crimes are discussed. By taking campus violence cases as examples, the major influencing factors of violent crimes are found through data analysis. The results show that campus violence cases are usually caused by the complex surrounding environments and persons. Also, campus security measures only cover a small range, and the security management is difficult. In the meantime, due to the younger ages and lack of self-protection awareness, students may easily become the targets of criminals. Therefore, the results have a positive significance for authorities to analyse the crime rates in a determinate area and take preventive measures against violent crimes.

This Article aims at the current high idle rate of landscaped gardens and a single overall style. The article inputs the quantitative relationship programming of the dynamic model of the urban landscape ecological city system into the Grasshopper software to obtain the urban landscape parameter growth curve, and at the same time applies the nonlinear parameterized model method to the landscape design. The research found that the feature form of the landscape garden presented in the thesis is mainly based on the nonlinear transformation of the local analysis structure feature. In the end, the thesis deeply researches the existing operating modes based on the concept of nonlinear thinking. Furthermore, it combines with information technology to supplement and update the traditional landscape construction from different perspectives.

This article introduces an improved sales percentage method to quantitatively calculate the evaluation process of the corporate sales cash flow percentage method in order to obtain more evidence-based financial data and increase the accuracy of the evaluation results. At the same time, the paper uses SPSS to perform regression analysis on related financial indicators and sales revenue and obtains quadratic regression equations and linear regression equations. The thesis predicts other financial index data based on the predicted future sales revenue, uses the revised linear regression equation to obtain the company's future net cash flow and calculates the company value.

This paper uses the finite element method to explain the specific nature of numerical instability such as network dependence in the topology optimisation of engineering structures from the perspective of partial differential equations. Gaussian function filtering method reduces the global impact of local extremum on topology optimisation. Finally, the method is introduced into the topology optimisation of concrete gravity dams in hydraulic engineering, and the topology optimisation program is developed in conjunction with ANSYS software language to achieve the topology optimisation of building structures in hydraulic engineering from a technical perspective.

Condensing the multi-dimensional digital model of green urban design, and constructing a digital method system of it progressively layer by layer. Based on this research background, the dissertation designs the spatial form of landscape architecture based on the data visualisation of nonlinear technology. The article uses the colour zoning method to design the actual scene of the garden landscape with nonlinear parameteriszation. The simulation result analyses that the proposed nonlinear algorithm has realised the efficiency improvement purpose of landscape architecture design.

Under the background of ‘mass entrepreneurship and innovation’, Chinese colleges and universities have strengthened students’ entrepreneurial and innovative abilities. The article first analyses the reasons why applied universities should strengthen innovation and entrepreneurship education. On this basis, the evaluation index system of students’ innovation and entrepreneurship ability is constructed. The thesis uses the nonlinear structural model to complete the index weight setting. Finally, the paper verifies the effectiveness of the combined evaluation model through the data on innovation and entrepreneurship of college students in an university where applied. At the same time, the article proposes measures for optimising the ecological environment of innovation and entrepreneurship education for colleges and universities.

In order to explore the application of machine learning algorithm to intelligent analysis of big data in an artificial intelligence (AI) environment, make cognitive computing meet the requirements of AI and better assist humans to carry out data analysis, first, the theoretical basis of machine learning algorithm is elaborated. Then, a cognitive computational model based on the machine learning algorithm is proposed, including the essence, principle, function, training method of deep belief network (DBN) algorithm, as well as the joint use of DBN algorithm and multilayer perceptron. Finally, the proposed algorithm is simulated. The results show that under the same parameter conditions, the accuracy rate of the DBN algorithm combined with multilayer perceptron is higher than that of the DBN algorithm; when the number of units is >40, the accuracy rate of the DBN algorithm combined with multilayer perceptron is significantly higher than that of the DBN algorithm; when the number of units is 30, the best effect can be obtained, and the error rate is <0.05, but the DBN algorithm cannot achieve this effect alone; when the number of network layers is specified as four, the error rate of the DBN algorithm combined with multilayer perceptron is <0.05, forming the optimal level. In the AI environment, the performance of the cognitive computational model based on the DBN algorithm and multilayer perceptron can reach the highest level, which makes the computer become a handy intelligent auxiliary tool for human beings.

The dichotomy model of education informatisation is essential, which means the measurement of education informatisation construction and development. Finite element differential equations play an essential role in signal and information teaching. To improve teaching information, the paper applies the dichotomy model of finite element differential equations to the reform of physics education information teaching. This article fully introduces the basic principles of the dichotomy model in finite element differential equations and introduces several analysis methods of the inverse Laplace transform of differential equations. At last, the method is applied to the informatisation of physics education to improve the quality of teaching.

The paper relies on the practice process of entrepreneurship education in colleges and universities to carry out research. It summarizes the optimal models suitable for students’ employment and entrepreneurship based on statistical analysis using the probability theory. We built a pyramid structured model of college students’ entrepreneurial ability based on this model. The thesis uses statistical methods to carry out a factor analysis of various abilities. It provides a basis for the adjustment and implementation of employment-oriented entrepreneurship education models in colleges and universities.

In order to consider many uncertain factors in the process of shot-put, a fuzzy optimisation model of shot-put is proposed. With the help of fuzzy anthropometric data and strength data, the model calculates the fuzzy solution set of the athlete's best throwing mode and throwing distance with a known probability distribution, which reflects the actual process of shot throwing better than the non-fuzzy optimisation model. Then, using MATLAB6 software, the program design of the model solving and the user interface of optimisation software are developed, which realises fast calculation and good user interaction function. Finally, the actual measurement data of university shot-putters are used to verify the feasibility and effectiveness of the fuzzy optimisation model.

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.

The advancement of Chinese education informatisation construction has injected new vitality into the development of Chinese educational technology in the new era and brought new challenges to the development of Chinese educational technology. Nonlinear dissipative structure theory has been a necessary enlightenment for the development of education informatisation. Based on the theory of nonlinear dissipative structure, the paper explores the relationship between the theory and education and teaching. It constructs a diversified regression calculation model of the information-based teaching ecology. Finally, it points out the strategies and ways to apply the dissipative structure theory to improve information-based teaching.

This article takes the nonlinear differential equation model as an example and uses information technology to create a new course teaching model. The computing software Maple is effectively applied to the precise solution of nonlinear differential equations through the analysis of examples. The overall goal and specific implementation of the teaching plan to integrate ordinary differential equations and information technology have been completed. The study found that the teaching plan proposed in the article is assisted by information technology, with teachers and students participating in an interactive and exploratory teaching method. This method is worthy of further promotion.

In order to solve the problem of the easy appearance of blurring images (easy to appear blur) or jagged effect after correction by traditional method, and as the visual error correction effect is not good, we propose a new visual error correction method of continuous calisthenics action image and a new algorithm for visual error correction. The continuous calisthenics action image is encoded and decoded, the error between the original image and the error image is obtained and with that the difference function is processed. Then the error compensation results are obtained and the visual error correction of the continuous calisthenics action image is realised. At the same time, a new algorithm for checking and correcting visual parallax matching errors is proposed in this paper. This algorithm can not only identify all matching errors in the parallax data, but also detect and correct them according to the continuity of shape representation, and effectively calculate the various performances of such matching algorithms automatically and quantitatively. The results show that the image processed by the proposed method has no significant visual error, and the peak signal-to-noise ratio and structural similarity are very high. The experimental results of the new algorithm also prove that the algorithm is very useful for the study of visual matching. It can be seen that the proposed method is effective and can be effectively used.

In order to discuss the application and mode of the forced modulation function in a sensor, the optical fibre emphasis function was established by referring to the geometric method, the tilt factor and the shape factor of the reflecting surface. These were introduced for the first time, and the corresponding mathematical model was established. The method of numerical simulation is systematically studied and multimode optical fibre parameters (including optical fibre of axial spacing, optical fibre core diameter and numerical aperture) are adopted. The reflective surface inclination and shape factors on the RIM–FOS intensity modulation characteristics are studied according to the obtained light quasi-Gaussian distribution model, establishing a general three-intensity modulation function of fibre optic sensor. The results show that the intensity modulation characteristic of specular reflection is obviously better than that of the diffuse reflection surface, and the peak value of the modulation function is five times that of diffuse reflection. The intensity modulation characteristic decreases with increase in the roughness of the reflection surface. The system can not only complete the RIM–FOS characteristic simulation and characteristic testing functions, but can also start-up the test and not be affected by the ambient light interference and power fluctuation of the light source. The test stability is good with high repeatability.

In order to improve the modelling efficiency in dynamic system prediction, this paper proposes a predictive model based on high-order normal differential equations to model high-order differential data to obtain an explicit model. The high-order constant differential equation model is reduced, and the numerical method is used to solve the predictive value. The results show that the method realises the synchronisation of model establishment and parameter optimisation, and greatly enhances the modelling efficiency.

In order to accurately describe the risk dependence structure and correlation between financial variables, carry out scientific financial risk assessment, and provide the basis for accurate financial decision-making, first the basic theory of Copula function is established and the mixed Copula model is constructed. Then the hybrid Copula model is nested in a hidden Markov model (HMM), the risk dependences among banking, insurance, securities and trust industries are analysed, and the Copula–Garch model is constructed for empirical analysis of investment portfolio. Finally, the deep learning Markov model is adopted to predict the financial index. The results show that the mixed Copula model based on HMM is more effective than the single Copula and the mixed Copula models. The empirical structure shows that among the four major financial industries in China, the banking and insurance industries have strong interdependence and high probability of risk contagion. The investment failure rate under 95%, 97.5% and 99% confidence intervals calculated by Copula–Garch model are 4.53%, 2.17% and 1.08%, respectively. Moreover, the errors of deep learning Markov model in stock price prediction of Shanghai Pudong Development Bank (sh600000), Guizhou Moutai (sh600519) and China Ping An Insurance (sh601318) are 2.56%, 2.98% and 3.56% respectively, which indicates that the four major financial industries in China have strong interdependence and risk contagion, so that the macro or systemic risks may arise, and the deep-learning Markov model can be adopted to predict the stock prices.

The article proposes a human motion capture method based on operational data. The thesis first uses the human body wear system to perform functional processing on the captured periodic motion data, and then extracts the data sequence for the few motions. Thereafter, the classification of the vector calculation method is carried out according to the characteristics of periodic data. Through experimental research, it is found that the functional data analysis (FDA) algorithm proposed in the thesis can accurately identify human motion behaviour, and the automatically collected data has a recognition rate that is as high as 98.9%. Therefore, we have concluded that the human body data functional analysis algorithm has higher recognition accuracy than the traditional optical capture system. Thus, it is worthy of further research and discussion.