In recent years, the advantage of cheap labour in China has gradually disappeared, and the economic development mode relying on resource consumption and low labour cost is facing numerous challenges. According to the law of economic market development, education progress is the most effective way to promote economic development, and it is also the only way to improve production efficiency [1, 2]. Only by playing the role of education, can we turn the progress of education into the driving force of development, thus playing an effective role in promoting development in the socialist market economy with Chinese characteristics. Among them, the implementation of ideological and political education (IPE) is often ignored; as the main battlefield of production, operation and management, higher vocational colleges have a far-reaching impact on the promotion of industrial upgrading and economic transformation [3]. As China’s economic development has entered the stage from high-speed growth to high-quality development, higher requirements are needed for applied talents; therefore, it is an important move to train technical talents with high moral and technical skills through ideological and political teaching, so as to enhance the driving force of China’s economic development [4, 5].

Nowadays, in higher education system, the homogenisation of education is more serious, which directly leads to the difficulty in meeting the needs of social talents for the output of university education, thus making the development of regional economy lag behind [6]. In addition, in the Western region, the level of ideological and political identity among college students in minority areas is low, which has seriously restricted the regional talent training and economic development [7, 8]. In the future, IPE will be conducive to promote economic growth and become a vital force to improve social production.

In order to develop higher education, we must rely on continuous investment in education funds. Only sustained and numerous investment can support the material demand and strategic change of IPE, which is related to the future development of the whole country, so it must be the focus of financial security [9, 10]. Therefore, it is of great significance to advance the level of regional IPE and stimulate the development of regional economy.

Under the background of multiculturalism, the innovation of IPE in colleges and universities has adhered to the basic principles of flat development and diversified practice, which fully absorbed advanced educational ideas in multi-cultural, so as to enhance the advancement and foresight of IPE and ensure that the IPE work in colleges can play a positive role in education and guidance, which should be carried out with high efficiency. Through the summary and analysis, IPE in colleges in China has the characteristics of a development stage, as shown in Figure 1.

As can be seen from Figure 1, at present, the popularisation of IPE in colleges has gradually increased. Under the current economic background, by combining with the national development strategy and based on the needs of economic development, an in-depth study of economic thought in the new era has been constantly integrated into the IPE and its internal management, decision-making mechanism, and teaching form and so has undergone multiple changes.

Improvement of the education level is closely related to the development of economy [11]. As shown in Figure 2, there are many different funding channels for higher education in China, including special expenditure of the state finance, donations from social organisations and organisations, funds from many private schools, business income and other sources.

In addition, there are also some sources of income, which are from the investment of schools, and the funds paid by the units subordinate to the schools. To sum up, we can divide the five funds mentioned in Figure 2 into two types according to whether they are allocated by the government finance: financial education funds and non-financial education funds. As the total amount of education funds is concerned, due to the higher degree of attention and the better and better level of economic development, the funds invested in higher education are constantly increasing [12].

The development of IPE can provide numerous high-level talents for the society and improve intellectual support for social development. Therefore, the long-term and sustained development of higher education is the top priority of future work, which needs continuous investment to ensure the advance of higher education, thereby providing human capital for the society. The internal relationship between IPE investment and economic growth is shown in Figure 3.

In the incremental investment analysis method, education investment can be regarded as human capital, which can promote economic growth. In the calculation of specific contribution rate (CR), economic growth should be regarded as the output rate and education investment as the capital item [13,14]. The analysis process of this method firstly finds out the growth surplus according to the production function, uses the counterfactual measurement method to obtain the increment of education investment, finally calculates the contribution of education to the growth of national income through the rate of return on education investment. Many scholars regard capital as the only factor to promote economic development and apply it to the construction of production function, but they could not obtain the obvious relationship between IPE and economic growth. Therefore, this study adopts the improved fuzzy clustering algorithm to establish the calculation model of the CR of China’s IPE.

Cluster analysis is an important data analysis method used to gather a certain class of the same things together to study and then analyse their overall characteristics and differences [15,16]. Fuzzy clustering analysis introduces fuzzy functions into clustering analysis, and through the similarity between data samples, the data sets are divided into several common data sets, and the membership degree of data samples to each class is given. The calculation principle is as follows:

Assume data set _{1}, _{2}, … , _{n}^{s}^{s}_{j}_{j1}, _{j2}, … , _{js}^{s}_{jk}_{j}

Fuzzy clustering of sample data sets is to divide the set _{i}_{ij}_{c×n} ∈ ^{c×n}, and the membership degree of sample data _{j}_{i}_{ij}

Make _{1}, _{2}, … ,_{c}_{1}, _{2}, … ,_{c}

At present, the existing fuzzy clustering algorithms are improved on the basis of existing clustering algorithms, such as fuzzy C-means clustering algorithm and fuzzy spectrum clustering algorithm, but these algorithms have the following shortcomings:

The number of clusters must be given, which reduces the credibility of the classification results.

The classification algorithm has high requirements on the objective function; is sensitive to the selection of initial value, which is easy to fall into local optimum; and is difficult to achieve the global optimum.

Therefore, in this study, the gravity search method is used to optimise fuzzy clustering, and the genetic algorithm is used to determine the classification data sets in the eastern, western and central regions of China. The calculation principle of the gravity search method is as follows:

Central force optimisation is an evolutionary algorithm based on Newton’s law of universal gravitation. The core formula of the algorithm is as follows:

In _{p}_{k}_{pk,t}_{pk,t}_{pk,t}_{k}_{pk,t}_{pk,t}_{k}

The introduction of the criterion can better determine the optimal classification number

The calculation of tightness is too arbitrary. The distance between the sample data and its class centre is taken as the measure of compactness. In extreme cases, when the number of categories approaches the number of sample data, the distance between the sample data and its class centre decreases monotonously and tends to zero, thus making compactness lose its due utility.

The topological structure of the sample data set is not considered. When two classes have overlapping data or no overlapping data, their class spacing may be equal, and the existing separation formula is indistinguishable.

Therefore, in this study, the classification number is adaptively determined by using the genetic algorithm, and the criterion function is optimised by using the gravity search method. The specific steps of the algorithm are shown in Figure 4.

Step 1. Initialise

Step 2. Convert

Step 3. Randomly generate a population _{1}, _{2} … , _{m}_{l}_{l}

Step 4. Calculate the membership degree of each individual according to formula (1) such that

Step 5. If

Step 6. Take the reciprocal of formula (1) as a fitness function and select individuals to enter the next-generation population, according to the principle of greed;

Step 7. Update the individual velocity and acceleration vector according to formula (5);

Step 8. Calculate the fitness function ^{*}, ^{*}, ^{i}

Step 9. Seek optimal solution of max^{*}, ^{*}, _{i}^{*}, ^{*},

From the perspective of algorithm design, giving the upper and lower bounds of classification numbers is helpful to improve the efficiency of the algorithm. Obviously, the lower bound of the classification number is 1. Considering that China is divided into seven parts, geographically, it is appropriate to define the upper bound of the classification number as 7. Numerical experiments are completed based on the aforementioned example information by utilising the proposed algorithm, and the boundaries of the algorithm are set as follows [19]: the value range of ^{−4}; the population size is 20, the crossover probability is 70%, the mutation probability is 0.5%, and the evolution algebra is 100; in addition, ^{−t/Tmax}, where T_{max} is the largest evolutionary algebra with a value of 100.

According to the China Statistical Yearbook (2014–2020 edition), the annual GDP, fixed asset investment, household consumption level, and employment population data of each province are obtained, and the algorithm mentioned before is used for regional classification. The results are shown in Table 1.

Classification results of provinces.

A | Sichuan, Zhejiang, Shandong, Guangdong |

B | Shaanxi, Xinjiang, Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Guangxi, Yunnan, Henan Hunan, Hebei |

C | Tibet, Gansu, Qinghai, Ningxia, Guizhou |

As can be seen from Table 1, Tibet, Gansu, Qinghai, Ningxia and Guizhou are located in the border areas, with weak industrial foundation, low population base, large proportion of agricultural population, relatively backward level of higher education and IPE, which belong to the least-developed areas in China, and their overall economic level is relatively backward, which requires special attention.

_{Ai}

Similarly, the CR of the labour input, material capital input and human capital input in the

_{Aj}

Similarly, the CR of material capital investment in each region is given as follows:

The CR of labour capital investment in each region is as follows:

The calculation of the CR of IPE progress is represented as _{A}

Among them, _{j}

The calculation process of the CR of IPE is shown in Figure 5.

Data acquisition: According to the production factors in the calculation model, data are collected, and sample data of each production factor and the sample data classified according to the level of educational progress are obtained.

Elastic coefficient estimation: The elastic coefficient of material capital investment in different regions is estimated by using the regression method, where _{i}_{i}_{i}

Calculate the progress rate of IPE. Firstly, the annual average growth rates of output, material capital, labour force and human capital of various regions are calculated according to formulas (11) – (14); Then, according to the Solow value equation in the combination model, the progress rate of IPE in each region _{i}

It is found that education and economic development are inseparable. Therefore, education is regarded as an element of economic development [20]. By adding the input structure in the calculation model, the model is decomposed to measure the contribution of IPE investment to economic growth. Assuming that the labour input is

Among them, _{0} is input of IPE personnel,

Take logarithm of both sides of the aforementioned formula, Formula (16) can be obtained:

Then take the full differential of both sides with respect to time

In order to more intuitively reflect the CR of IPE to the economy, this article uses the difference quotient formula to separate the factors that affect the growth rate, and then the difference quotient is used to discretise the growth rate equation as follows:

The model of the contribution of IPE education to economic growth rate is as follows:

Among them, _{ε}_{ε}

Under actual circumstances, it is difficult to estimate _{ε}_{ε}

According to the 2014–2020 edition of the China Statistical Yearbook, the annual GDP, fixed assets investment, household consumption level and employment population data of each province, as well as the statistical data of teaching efficiency and IPE quality of colleges and universities in various regions, are used the this model. The influencing factors of the CR of higher education to economic growth selected in this study are the number of students enrolled, the number of teachers and students in school, the investment scale of IPE and the number of special projects of IPE.

Although some scholars have considered the turnover rate of graduates, after analysing the system dynamics simulation model, the results show that the relative error between simulation results and actual results is only 7.33%. In addition, the data statistics of turnover rate in China are not comprehensive, so the influence of other factors such as brain turnover rate is not considered in this study.

Figure 6 reflects the CR of IPE progress in A, B and C areas, with average values of 8.46%, 5.38% and 1.99%, respectively. At present, the development of IPE in China is unbalanced among regions, with the highest level of education in class A, far exceeding that in classes B and C. Therefore, we should vigorously speed up the construction of IPE in classes B and C, implement better preferential policies and subsidy policies and guide social investment, so as to realise the common progress of higher education in all areas.

In order to more intuitively analyse the CR of IPE in different regions of China, the CR of IPE in eastern, western and central regions is compared, and the results are shown in Table 2.

Comparison of CRs of IPE in eastern, western and central regions.

_{ε} |
_{ε} |
||||

Central China | Shaanxi | 4.27 | Eastern China | Shanghai | 8.34 |

Inner Mongolia | 3.42 | Zhejiang | 6.45 | ||

Anhui | 5.82 | Tianjin | 4.56 | ||

Hunan | 8.23 | Jiangsu | 7.33 | ||

Hubei | 6.33 | Guangdong | 7.09 | ||

Henan | 5.20 | Beijing | 13.98 | ||

Jilin | 5.73 | Liaoning | 5.80 | ||

Western China | |||||

_{ε} |
_{ε} |
_{ε} |
|||

Sichuan | 6.31 | Tibet | 1.02 | Qinghai | 1.28 |

Yunnan | 3.20 | Shaanxi | 1.24 | Xinjiang | 0.93 |

Guizhou | 2.83 | Gansu | 2.49 | Guangxi | 3.01 |

CRs, contribution rates; IPE, ideological and political education.

The level of IPE in eastern China is far higher than that in other parts of China, especially in Beijing, Shanghai and Jiangsu. At the same time, it is easy to find that these areas with a high level of higher education are also economically developed areas. Although the absolute CR of other provinces is not high, considering the economic strength of these provinces, its educational output is much higher than that of the central and western regions. In addition, the CR of the central and western regions is far lower than that of the eastern developed regions, which also shows that the CR of IPE between the two regions is greatly different due to the huge gap in economic strength.

Also, it can be seen from Table 2 that Hunan and Sichuan, as depressions of higher education, have accumulated rich educational resources, so the CR of IPE can maintain a steady and rapid growth. However, Guizhou, as a remote and poor area, has very scarce higher education resources, so the CR of IPE is very small, but it can also maintain a small growth with the economic development which also shows that it has a huge development space, as long as the investment in education is increased, the CR of education will be greatly improved.

Vigorously promoting the construction of IPE in various regions is the key to cultivating high-quality talents, which is also an important measure to strengthen the internal driving force of China’s economic development. Therefore, this article introduces the investment of IPE into the function model of social production, where fuzzy clustering is optimised by using the gravity search method, and the classified data sets of various provinces in China are determined by using the genetic algorithm. Based on the improved fuzzy clustering algorithm, the calculation model of the CR of IPE in different regions is established. The results show that at present, the development of IPE in China is unbalanced among regions, and the average CRs of IPE in A, B and C regions are 8.46%, 5.38% and 1.99%, respectively. Due to the huge gap in economic strength, the CR of the central and western regions is far lower than that of the eastern developed regions, but some of them are rich in educational resources and have great development potential, whose investment on IPE should be increased in the future.

#### Comparison of CRs of IPE in eastern, western and central regions.

_{ε} |
_{ε} |
||||

Central China | Shaanxi | 4.27 | Eastern China | Shanghai | 8.34 |

Inner Mongolia | 3.42 | Zhejiang | 6.45 | ||

Anhui | 5.82 | Tianjin | 4.56 | ||

Hunan | 8.23 | Jiangsu | 7.33 | ||

Hubei | 6.33 | Guangdong | 7.09 | ||

Henan | 5.20 | Beijing | 13.98 | ||

Jilin | 5.73 | Liaoning | 5.80 | ||

Western China | |||||

_{ε} |
_{ε} |
_{ε} |
|||

Sichuan | 6.31 | Tibet | 1.02 | Qinghai | 1.28 |

Yunnan | 3.20 | Shaanxi | 1.24 | Xinjiang | 0.93 |

Guizhou | 2.83 | Gansu | 2.49 | Guangxi | 3.01 |

#### Classification results of provinces.

A | Sichuan, Zhejiang, Shandong, Guangdong |

B | Shaanxi, Xinjiang, Shanxi, Inner Mongolia, Jilin, Heilongjiang, Anhui, Jiangxi, Guangxi, Yunnan, Henan Hunan, Hebei |

C | Tibet, Gansu, Qinghai, Ningxia, Guizhou |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Research and implementation of smart city public information mining analysis system based on mobile edge model of game theory Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Design of college education evaluation based on accompanying data acquisition and mathematical analysis Enterprise financial strategy and performance management analysis based on principal component analysis Study on the Dynamic Change of Regional Water Level and Climate Based on Forecast Equation Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Municipal Civil Engineering Construction Based on Finite Element Differential Equations Financial Risk Prevention Model of Financial Institutions Based on Linear Partial Differential Equation Influence of heterogeneity of local officials on the economy of resource-based cities developed with high quality Analysis of influencing factors of SPOC course teaching effect using structural equation modelling Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation Research on the construction of rural interface style based on aesthetic rules Optimization Algorithm of New Media Hot Event Push Based on Nonlinear Differential Equation Mathematical Differential Equation in Calculating the Strength of Building Beam Structure Impact Resistance Stability of Building Structural Engineering Based on Fractional Differential Equations The Technical Research on the Assessment of Network Security Situation Based on D-S Evidence Theory Computer big data modeling system based on finite element mathematical equation simulation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation Uniqueness of system integration scheme of artificial intelligence technology in fractional differential mathematical equation The Composition System of Pop Music Movement Based on Finite Element Differential Equations The Structure and Influencing Factors of Innovation and Entrepreneurship Ability of Higher Vocational Students Based on Structural Equation Model Model System Study of Accordion Score Based on Fractional Differential Equations Data mining of Chain convenience stores location Parameter Id of Metal Hi-pressure State Equation P-Matrix Reasoning and Information Intelligent Mining Research on Detection Model of Abnormal Data in Engineering Cost List Research on deformation monitoring of tunnel engineering based on 3D laser scanning Solidification treatment effect of wellsite waste mud based on physical adsorption of a composite curing agent A study of immersive technology for product usability improvement design based on comprehensive value evaluation Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Optimal Research in Piano Shape Sound and Sound Propagation Model Based on Nonlinear Differential Equations Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Badminton players’ trajectory under numerical calculation method Mathematical methodology in the seismic resilience evaluation of the water supply system Prediction of surface quality in end milling based on modified convolutional recurrent neural network Analysis of IPO pricing efficiency under the registration system Case application data research of traditional ink art elements in packaging design Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data Application of intelligent teaching resource organisation model and construction of performance evaluation model Secure transmission of simultaneous wireless information and power transfer system for Internet of things Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Numerical simulation of vortex vibration in main girder of cable-stayed bridge based on bidirectional fluid–structure coupling Research on location algorithm of new energy vehicle charging station based on multi-objective decision Optimisation of construction mode of residential houses based on the genetic algorithm under BIM technology A study on the reform of college English education inspired by the cultural differences between China and the United States Research on innovative strategies of college students’ English teaching under the blessing of big data Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption Attitude control for the rigid spacecraft with the improved extended state observer A long command subsequence algorithm for manufacturing industry recommendation systems with similarity connection technology Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Evaluation of spoken English self-study system considering speech knowledge recognition algorithm Application research on piano teaching in colleges and universities based on remote wireless network communication Construction of Financial Risk Evaluation Index System for Biomass Graphene Fibre Industrialisation Project System dynamics model of output of ball mill Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Design of Morlet wavelet neural network to solve the non-linear influenza disease system An online statistical analysis of the hotel management and operation performance model Research on the post-purchase behaviour tendency of the product quality to customers in fast-selling marketing Motion about equilibrium points in the Jupiter-Europa system with oblateness Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA Optimal preview repetitive control for impulse-free continuous-time descriptor systems Design of information management system based on wireless communication under the background of Internet of Things The impact of global warming on the small Scottish Fishing Company Development of main functional modules for MVB and its application in rail transit Analysis of agricultural economic development and optimisation measures under the strategy of rural revitalisation Study on the impact of forest fire prevention policy on the health of forest resources Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Research on the relationship between government subsidies, R&D investment and high-quality development of manufacturing industry Research on the protection and inheritance of intangible cultural heritage under the background of rural revitalisation Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model Computer vision recognition and tracking algorithm based on convolutional neural network A review of the treatment techniques of VOC Study on structural parameter design and life analysis of large four-point contact ball bearing channel Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}Digital marketing solutions based on consumer data and homomorphic encryption The consistency method of linguistic information and other four preference information in group decision-making Statistical Model of College Ideological and Political Learning Based on Fractional Differential Equations Research on the driving principle and guiding strategy of the public's collaborative supervision of the sharing economy in my country Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development Nonlinear Differential Equation in Anti-aging Test of Polymer Nanomaterials Application research of bel canto performance based on artificial intelligence technology Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Application of regression function model based on panel data in financial risk management of bank resource allocation Application of knowledge graph in smart grid fault diagnosis University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation Research on the optimisation of logistics parcel intelligent sorting and conveying chain combined with variable clustering mathematical method Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Research on Resonance Properties of Semantic Wave Fractal Fractals Based on Quantitative Analysis of English Corpus Research on urban landscape big data information processing system based on ordinary differential equations Modeling of fractional differential equation in cloud computing image fusion algorithm Application of Discriminative Training Algorithm Based on Intelligent Computing in English Translation Evaluation Research on the application of GLE teaching mode in English-medium colleges The application of directional derivative in the design of animation characters and background elements Research on product process design and optimisation model based on IoT intelligent computing Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education LTE wireless network coverage optimisation based on corrected propagation model The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform Study on tourism development income index calculation of finite element ordinary differential mathematical equation The Security of Database Network Model Based on Fractional Differential Equations Electric Vehicle Mechanical Transmission System Based on Fractional Differential Equations The Practice System of Physics and Electronics Courses in Higher Vocational Colleges Based on Fractional Differential Equations The Economic Model of Rural Supply and Demand Under the Data Analysis Function Based on Ordered Probit 3D Modeling System of Indoor Environment Art Landscape Design under Statistical Equation Electronic Information Security Model of Nonlinear Differential Equations The Optimization Model of College Students' Physical Exercise Motivation and Self-control Ability Based on the Mathematical Model of Probability Theory Paris panxiensis , a new combination of Trilliaceae from Sichuan, ChinaImpact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas Criminal law imputation path for biometric information Research on composite dynamic disaster prevention and control system of mine earthquake and shock in thick and hard rock mines Research on innovative strategies of college students’ English teaching under the background of artificial intelligence Electromagnetic interference prediction technology of new energy motor drive system Research on the application of PLC technology in electrical automation engineering Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Application of matrix multiplication in signal sensor image perception Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Analysing the variation of metadiscourse verb patterns in English academic papers from within and between disciplines Impact of COVID-19 policy on stock prices of listed property companies Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation Research on the experimental principle of deep integration of LETS software and criminal procedure under the background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic expression of paper-cut elements in the design of boat space Knowledge graph construction and Internet of Things optimisation for power grid data knowledge extraction Modeling the pathway of breast cancer in the Middle East Construction and intelligent analysis of power grid physical data knowledge graph based on Internet of Things for power system Research on industrial Internet of Things and power grid technology application based on knowledge graph and data asset relationship model Research on the effects of financial literacy on rural household credit constraint Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on educational resource recommendation system based on MRLG Rec The Mathematical Analysis Model of Educational System in Music Courses in Colleges and Universities Continuing Education Network Data Center Model Based on Fractional Differential Mathematical Equations A study on the phenomenon of anaphoric correction in college students’ English conversation Computer Art Design Model Based on Nonlinear Fractional Differential Equations The Optimization Model of Public Space Design Teaching Reform Based on Fractional Differential Equations The Approximate Solution of Nonlinear Vibration of Tennis Based on Nonlinear Vibration Differential Equation Graphical Modular Power Technology of Distribution Network Based on Machine Learning Statistical Mathematical Equation Employment and Professional Education Training System of College Graduates Based on the Law of Large Numbers Economic Research on Multiple Linear Regression in Fruit Market inspection and Management Nonlinear Differential Equations in Preventing Financial Risks Lagrange’s Mathematical Equations in the Sports Training of College Students Simulation Research of Electrostatic Precipitator Power Supply Voltage Control System Based on Finite Element Differential Equation Research on the effect of generative adversarial network based on wavelet transform hidden Markov model on face creation and classification Research on Lightweight Injection Molding (CAE) and Numerical Simulation Calculate of New Energy Vehicle Power Flow Calculation in Smart Distribution Network Based on Power Machine Learning Based on Fractional Differential Equations Demonstration of application program of logistics public information management platform based on fuzzy constrained programming mathematical model Basketball Shooting Rate Based on Multiple Regression Logical-Mathematical Algorithm The Optimal Application of Lagrangian Mathematical Equations in Computer Data Analysis Similarity Solutions of the Surface Waves Equation in (2+1) Dimensions and Bifurcation Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Limit cycles of a generalised Mathieu differential system Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Application of data mining in basketball statistics The nonlinear effects of ageing on national savings rate – An Empirical Study based on threshold model Design of fitness walker for the elderly based on ergonomic SAPAD model AtanK-A New SVM Kernel for Classification Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Study of a linear-physical-programming-based approach for web service selection under uncertain service quality The Relationship Between College Students’ Taekwondo Courses and College Health Based on Mathematical Statistics Equations Analysis and countermeasures of cultivating independent learning ability in colleges teaching English based on OBE theory A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Fractional Differential Equations in the Exploration of Geological and Mineral Construction AdaBoost Algorithm in Trustworthy Network for Anomaly Intrusion Detection Projection of Early Warning Identification of Hazardous Sources of Gas Explosion Accidents in Coal Mines Based on NTM Deep Learning Network Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Enterprise Financial Risk Early Warning System Based on Structural Equation Model A Study on the Application of Quantile Regression Equation in Forecasting Financial Value at Risk in Financial Markets Fractional Differential Equations in the Model of Vocational Education and Teaching Practice Environment Information transmission simulation of Internet of things communication nodes under collision free probability equation Image denoising model based on improved fractional calculus mathematical equation Random Fourier Approximation of the Kernel Function in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential Equations The Law of Large Numbers in Children's Education Optimization System of Strength and Flexibility Training in Aerobics Course Based on Lagrangian Mathematical Equation Data structure simulation for the reform of the teaching process of university computer courses RETRACTION NOTE Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Research on non-linear visual matching model under inherent constraints of images Good congruences on weakly U-abundant semigroups Can policy coordination facilitate unimpeded trade? An empirical study on factors influencing smooth trade along the Belt and Road Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Research on design of customer portrait system for E-commerce Research on rule extraction method based on concept lattice of intuitionistic fuzzy language Fed-UserPro: A user profile construction method based on federated learning A multi-factor Regression Equation-based Test of Fitness Maximal Aerobic Capacity in Athletes Design and evaluation of intelligent teaching system on basic movements in PE Garment Image Retrieval based on Grab Cut Auto Segmentation and Dominate Color Method Financial Risk Prediction and Analysis Based on Nonlinear Differential Equations Constructivist Learning Method of Ordinary Differential Equations in College Mathematics Teaching Multiple Effects Analysis of Hangzhou Issuing Digital Consumer Coupons Based on Simultaneous Equations of CDM Model Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations A Hybrid Computational Intelligence Method of Newton's Method and Genetic Algorithm for Solving Compatible Nonlinear Equations Pressure Image Recognition of Lying Positions Based on Multi-feature value Regularized Extreme Learning Algorithm English Intelligent Question Answering System Based on elliptic fitting equation Precision Machining Technology of Jewelry on CNC Machine Tool Based on Mathematical Modeling Application Research of Mathematica Software in Calculus Teaching Computer Vision Communication Technology in Mathematical Modeling Skills of Music Creation Based on Homogeneous First-Order Linear Partial Differential Equations Mathematical Statistics Technology in the Educational Grading System of Preschool Students Music Recommendation Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation 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 Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsThe internal mechanism of corporate social responsibility fulfillment affecting debt risk in China: analysis of intermediary transmission effect based on degree of debt concentration and product market competitive advantage Study on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Asymptotic stability problem of predator–prey system with linear diffusion Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network