Agricultural economy [1] is the foundation of the national economy and plays an important role in the development of the national economy, which cannot be replaced by other industries. Looking at the current situation of my country's agricultural development, it has the disadvantages of starting late with a relatively weak development level. The shortcomings of agricultural modernisation development directly drag down the overall process of my country's ‘four modernisations’ [2], Against the background of such a development environment, in order to make up for the insufficiency of agricultural development, the 19th National Congress of the Communist Party of China proposed a rural revitalisation strategy [3], adhering to the priority development of agriculture and rural areas [4]. The general requirements for effective governance and a prosperous life [5], establish and improve the urban-rural integrated development system [6] and policy system [7] and accelerate the modernisation of agriculture and rural areas. In order to develop agriculture, the optimisation of the industrial structure must be at the forefront. The speed of agricultural development directly determines the speed of the development of the secondary and tertiary industries. Therefore, it is even more important to optimise the industrial structure of agricultural economic development [8]. All points of entry to study its ways to promote rural revitalisation should be analysed.

Many experts and scholars in my country have made outstanding contributions to the research on promoting agricultural economic development and optimisation measures, and their professional research results have provided strong support for the development of modern agriculture. Some scholars believe that the optimisation of the agricultural industrial structure is the key to agricultural development in the new era [9], which not only plays a vital role in increasing farmers’ income but also meets the market's demand for agricultural products to a certain extent and realises the integration of the agricultural industry and market. Double coordination between [10]. Some scholars believe that the development of the agricultural industry cannot be limited to the current one [11], and the goal should be long term, realise dynamic monitoring [12], constantly adjust the influencing factors in the research process and even provide agricultural development through policy innovation. Other scholars proposed that the adjustment of the agricultural industry should be carried out in different levels and regions [13], organically combining the industrial structure, production structure, variety structure and other aspects [14] to find an excellent and feasible plan for each level, which promotes agricultural economic development [15].

On the basis of summarising and studying related theories, this paper deeply discusses the research results of the predecessors, starting from the significance of agricultural economic development, and analyses the advantages of optimising the agricultural industrial structure for agricultural development under the strategy of rural revitalisation [16]. According to relevant research, the agricultural industrial structure optimisation measurement index system was constructed, and according to the 22 specific indicators in the ‘Rural Revitalization Strategic Plan (2018–2022)’, the cointegration test was carried out through Eviws7.0 [17] and Granger causality test [18], using the analytic hierarchy process [19] and entropy method [20] to compare and analyse data, to measure the degree of rural revitalisation by the optimisation of the agricultural industrial structure [21], to analyse agricultural economic development of the optimisation strategy [22], and to strive to contribute a little to the overall layout of rural revitalisation.

Both social and economic development and natural development have certain laws to follow, and the forms of agricultural production and rural economic development are influenced by them to form a certain development model, that is, agricultural economy. The development of agricultural economy directly determines the income of farmers. If farmers want to get rich, they must develop agriculture and improve economic benefits. The proposal of the rural revitalisation strategy provides better policy support for the development of agriculture and rural economy. This theoretical background still needs further in-depth discussions by scholars to make up for the shortcomings in the field of agricultural science and technology in my country.

How to achieve the clear goals and requirements put forward by rural revitalisation? What are the ways? How should the results be evaluated? These are the issues that need to be discussed at present. Although many experts and scholars have achieved some results through their own study and efforts, these academic achievements are still far from enough on the road of rural revitalisation. The author discusses the agricultural economic development and optimisation measures under the rural revitalisation strategy and strives to find more abundant development paths for rural revitalisation, sort out new ideas, and further optimise the agricultural and rural industrial structure and improve the solution through rationalised data calculation and analysis. ability to deal with practical problems.

Rural revitalisation is the most favourable strategy proposed by the party and the state for rural development in the new era [23]. To realise the area of rural revitalisation, it is necessary to manage all aspects and achieve the goal through multiple channels. Judging from the current situation of agricultural development in my country, there are many agricultural practitioners and a wide range of areas, which can meet the demand for labour output to a certain extent. However, engaging in agricultural production also has the disadvantages of unstable returns, large risk fluctuations and long production cycles. Therefore, my country's agricultural development is at a disadvantage. With the continuous development of the social economy, the needs of agricultural economic development are also increasing day by day, and the inconsistency between the agricultural industrial structure and the requirements of agricultural development goals has become a major obstacle to development. Because the optimisation and reform of agricultural economic development is carried out in parallel, it is of practical significance to implement rural revitalisation and improve the level of agricultural economic development.

Since the time series in reality are mostly non-stationary, if the regression analysis is carried out directly, there will be a ‘pseudo-regression’ phenomenon, which will affect the research results. For cointegration analysis [24], the stationarity of the time series [25] needs to be checked, which proceeds as follows:

The cointegration test commonly used Engle-Granger cointegration test or Johansen cointegration test. The EG cointegration test is generally suitable for cointegration between two variables [26], and the Johansen cointegration test is generally used for cointegration between multiple variables. This paper is a test between multiple groups of two variables; so, the EG cointegration test is used [27]. This paper establishes a cointegration regression model to test the long-term equilibrium relationship between agricultural industrial structure optimisation and rural revitalisation [28]. This long-term equilibrium relationship is maintained by continuously adjusting short-term fluctuations; so, an error correction model (ECM) needs to be introduced [29] to be additional to that.

Among them is the explanatory variable lnx_{t}, where _{t}_{t} is the explained variable, where _{t}_{t}

The ECM is as follows:
_{0} is a constant term and, _{1}, _{1} is the random error amount.

The data are mainly from the 2001–2017 ‘A Statistical Yearbook’ and ‘A Government Work Report,’ and the official data are released by the city's bureau of statistics. This article selects reviews with 7.0 as the analysis tool for EG cointegration analysis, regression analysis and Granger causality test [30]. For the convenience of inspection, the data of each indicator are expressed as follows: the annual growth rate of agricultural output value (ZC), the comprehensive grain production capacity (LS), the proportion of rural employees engaged in non-agricultural industries (JS) and the agricultural labour productivity (LD), the growth rate of agricultural added value (XJ), the income ratio of urban and rural residents (CJ), the per capita net operating income of rural households (NJ), the Engel coefficient (NG) of rural residents and the proportion of rural residents’ expenditure on education, culture and entertainment (JY). According to the corresponding indicators in Figure 2, this paper will analyse the annual growth rate of agricultural output value and comprehensive grain production capacity (denoted as L4-1), the proportion of non-agricultural labour force and agricultural labour productivity (L4) among rural employees, the ratio of the growth rate of agricultural added value to the income of urban and rural residents (L4-3), the per capita net operating income of rural households and the Engel's coefficient of rural residents (L4-4) and the ratio of per capita net operating income of rural households to rural residents. The proportion of education, culture and entertainment expenditure (L4-5) is analysed in five groups of time series data. In order to ensure the accuracy and scientificity of the research and prevent the variables and numerical values from changing drastically, the logarithm of each group of data is used as a variable for research. LNZC, LNLS, LNJS, LNLD, LNXJ, LNCJ, LNNJ, LNNG, LNJY (logarithmic processing will not affect the nature of the data) are recorded, and the ADF test is performed. It can be seen that the labour force engaged in non-agricultural industries among the rural employees has gradually declined, and the number was the smallest in 2016, and the change in the labour generation rate after 2003 was small. The per capita net operating income of rural households and the Engel's coefficient of rural residents gradually decreased and reached their peaks in 2010. From Figure 4(a), it can be seen that the per capita operating net income of rural households has gradually increased, and the proportion of labour force has decreased. It shows that the living standard of rural residents has been improved.

The principle of the ADF test method is that the null hypothesis is that the sequence has a unit root, that is, non-stationary. When testing time series data, under the conditions of a given confidence level (1%, 5%, 10%), when the obtained statistic is significantly less than the critical statistical value of confidence, it means that the null hypothesis is rejected, that is, it is stationary; otherwise, it is non-stationary. The ADF test model is as follows:

The results of the data test for each group of variables:

Taking LNZC as an example, when the sequence LNZC has a constant term, a time trend term and a lag order, the ADF value is greater than the critical value at the 5% significance level, and the

If the linear combination of non-stationary time series is stationary, the combination reflects the existence of long-term stable relationship between variables.

Proportional relationship is also called as cointegration relationship. If the time series have the same single integer order, and some linear

If the combination (cointegration vector) reduces the single integer order of the combined time series, it is said that there is a significant cointegration relationship between these time series. From the analysis of the unit root test results, it can be known that LNZC, LNLS, LNJS, LNLD, LNXJ, LNCJ, LNNJ, LNNG, and LNJY are all first-order single integers; so, LNZC and LNLS, LNJS and LNLD and LNXJ and LNCJ can be performed; Engle-Granger cointegration tests can be performed between LNNJ, LNNG and LNJY. For the convenience of research, this paper directly uses the Eng1e-Granger test method in Eivews to test whether there is a long-term equilibrium relationship between each group of variable data. The long-term equilibrium equations for each group of variables are obtained as follows:

The residual sequence is saved, and the ADF test is performed on the residual sequence. The stationarity test results are shown in Table 1, which verifies the stability of the ADF residual test.

ADF variable residual test results

1 | −5.8 | −1.6 | Stable | |

2 | −2.3 | −1.9 | Stable | |

3 | −4.8 | −1.9 | Stable | |

4 | −3.1 | −1.9 | Stable | |

5 | −3.9 | −1.9 | Stable |

The cointegration test results show the annual growth rate of the total agricultural output value and the comprehensive grain production capacity of a city over the years, the proportion of rural employees engaged in non-agricultural industries and agricultural labour productivity, the growth rate of agricultural added value and the ratio of urban and rural residents’ income. There is a long-term equilibrium relationship between the per capita operating net income and the Engel coefficient of rural residents and the proportion of rural residents’ expenditure on education, culture and entertainment, which means that there is an ECM. The result is as follows:

The signs of the correction coefficients of ECM(−1) in each group are all negative, which conforms to the reverse correction mechanism. From the above test results, it can be seen that the residual

The principle of the Granger causality test is as follows: if variable X is the cause of the change in Y, then adding the lag of X to the regression can significantly improve the prediction of Y. The Granger causality test is ‘Granger causality’ in the statistical sense, and its test conclusion is only a prediction not a causal relationship in the true sense, but this does not hinder its reference value. In the regression model, some variables do not necessarily have a certain causal relationship but are significantly correlated. We have found through regression analysis that there is a long-term stable equilibrium relationship between the variables in each group. Therefore, the test of the causal relationship between variables is as follows: meaningful and necessary. The Granger causality test results for each group of variables are shown in Table 2, where F is the family income variable and P is the labour force variable.

Gran causality test results

1 | LNLS | 2.4 | 0.06 |

LNZC | 1.07 | 0.40 | |

2 | LNLD | 2.92 | 0.09 |

LNIS | 0.11 | 0.73 | |

3 | LNCI | 3.15 | 0.06 |

LNXJ | 0.21 | 0.82 | |

4 | LNNJ | 3.19 | 0.08 |

LNGJ | 1.63 | 0u.22 | |

5 | LNJY | 5.19 | 0.02 |

LNNJ | 5.54 | 0.03 |

As far as the model constructed in this paper is concerned, the rural revitalisation strategy is the reason for the optimisation of the industrial structure.

The tomographic analysis method has been applied by scholars as early as the 1970s. It is a method that combines qualitative and quantitative methods for hierarchical weight decision-making and an analysis to draw conclusions. AHP is suitable for solving a series of complex problems with many objectives, many criteria, difficult quantification and weak structural characteristics and provides simpler solutions for such problems. Hierarchical gaps can to a certain extent avoid the deviations caused by the subjective judgements of decision makers. It is a mistake in thinking to avoid decision makers from facing many criteria and problems. This is also an important reason why the analytic hierarchy process is used by many scholars.

For the assignment of importance, the scale method of 1–9 is usually used to construct an n-order judgement matrix. The scales at all levels are shown in Table 3.

Scales and meanings at all levels

1 | Equally important | 1 |

2 | Slightly important | 3 |

4 | Extremely important | 7 |

5 | Slightly unimportant | 9 |

6 | Obviously unimportant | 1/3 |

7 | Strong is not important | 1/5 |

8 | Extremely unimportant | 1/7 |

9 | In the middle | 2, 4, 6, 8 |

10 | In the middle | 1/2, 1/4, 1/6, 1/8 |

Because each index needs to be compared, it is necessary to standardise the elements of each column in the judgement matrix, using formula (8), where
_{ij}

Use formula (9) to calculate the weight of each element

Use formula (10) to calculate the maximum eigenroot of the judgement matrix:

Using formula (11),

Use formula (12) to calculate the consistency ratio, where

RI value

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.5 | 0.9 | 1.1 | 1.2 | 1.3 | 1.4 | 1.4 |

The concept of entropy originates from statistical physics and heat and is used to quantitatively describe the degree of uncertainty of a system. This paper uses the entropy method to determine the weight of each index, which provides the basis for quantitative analysis for comprehensive evaluation.

Due to the inconsistency of the measurement units of various indicators, it is impossible to compare them accurately and objectively. Therefore, before calculating specific indicators, it is necessary to convert the absolute value of the indicator into a relative value and let

Positive indicators:

Negative indicators:
_{ij}

For the first index _{ij}_{j}_{ij}_{j}_{max} = 1(_{ij}_{ij}_{j}_{j}_{j}_{j}

Among them, _{j}

Calculation results of entropy value of each index

Economic and social development level | Per capita GDP | 0.51 | 0.47 |

Per capita fiscal revenue | 0.79 | 0.16 | |

Proportion of tertiary industry | 0.69 | 0.28 | |

Total power of agricultural machinery | 0.65 | 0.34 | |

Grain yield per unit area | 0.72 | 0.25 | |

Urbanisation level | 0.74 | 0.22 | |

Per capita income of rural residents | 0.69 | 0.25 | |

Per capita cultivated land area | 0.77 | 0.24 | |

forest coverage | 0.71 | 0.26 | |

Industrial carbon dioxide emissions | 0.73 | 0.21 | |

Ecological environment security | Hydroxide emission | 0.79 | 0.20 |

Soot emission | 0.90 | 0.12 | |

Effective irrigation area | 0.82 | 0.17 | |

Fertiliser use intensity | 0.75 | 0.27 | |

Pesticide use intensity | 0.86 | 0.15 |

From the cointegration regression equation, there is a long-term equilibrium relationship between the indicators of agricultural industrial structure optimisation and rural revitalisation indicators, and from the results of the Granger causality test, the optimisation of agricultural industrial structure is the Granger cause of rural revitalisation. In terms of each group of indicators, it can be considered that the optimisation of the agricultural industrial structure has effectively promoted rural revitalisation. Among them, the promotion of the prosperity of the industry is the greatest. The specific performance is that the annual growth rate of the total agricultural output value increases by 1 unit, and the comprehensive grain production capacity increases by 0.22 units; the proportion of rural employees engaged in non-agricultural industries increases by 1 unit, and agricultural labour productivity rose by 0.35 units. Promoting the affluence of life comes second, as shown in the fact that the growth rate of agricultural added value increases by 1 unit, and the income ratio of urban and rural residents decreases by 0.12 units; the per capita operating net income of rural households increases by 1 unit, and the Engel coefficient of rural residents decreases by 0.24. units. Then, there is the rural style and civilisation. The per capita net operating income of rural households increased by 1 unit, and the proportion of rural residents’ expenditure on education, culture and entertainment decreased by 0.44 units.

Agricultural economy is an important part of my country's economic development. Relevant departments must strengthen their understanding of agricultural economic management work. Various situations in the economic development have contributed to the healthy and sustainable development of my country's rural economy.

The development of agricultural economy needs a strong theory as a support, which requires the establishment of a corresponding management mechanism. In the new era, driven by the rural revitalisation strategy, a systematic and institutionalised economic situation has gradually emerged. Relevant departments have also stepped up their efforts to continuously adjust and optimise the management mechanism based on the actual situation, promote industrial upgrading and then ensure the management system. It can match the reality of rural economic development and meet the diversified needs of agricultural economic development. In the process of optimising the management mechanism, the transformation of farmers’ production concepts is also an important part of agricultural economic development. Relevant departments should continuously disseminate advanced production concepts among farmers through training courses and on-the-spot explanations by experts to assist in optimising the management mechanism. In addition, it is necessary to continuously update agricultural production equipment. Farmers themselves and relevant departments must do their homework in this regard. Advanced equipment can improve the efficiency of agricultural production and create more production capacity within a certain period of time. The agricultural management department should exchange feedback with farmers to form a good connection so that the excellent management mechanism can truly take root and germinate in the fields, so as to better serve the development of the agricultural economy.

Science and technology are the boosters of all productive forces, and the continuous improvement of the level of science and technology is an effective means for the continuous development of my country's agricultural economy. The agricultural management department must learn advanced technical means before farmers, strengthen the work of agricultural economics and do a good job in the overall management of the standardised development of agriculture through the use of high-tech means. On this basis, agricultural management departments should also make scientific predictions on agricultural development, and based on this, they must formulate relevant policies to adapt to the general trend of agricultural economic development. It is necessary to give full play to the advantages of scientific and technological means, make scientific judgements through reasonable calculation, comparison and data analysis, change the traditional way of relying on experience and old farmers, establish and improve a networked supervision system and better solve problems in agricultural development, which is an outstanding issue.

The implementation of agricultural economic development work needs to rely on talents; talents are the carrier of management technology, and the quality of talents is directly related to the quality of agricultural economic development work. The management department should also regularly organise management personnel to carry out systematic work training to ensure the work quality and professional ethics of all personnel and always maintain the advanced level of management concepts and methods. The actual and future development directions of agricultural development in different regions are different. Managers in each region should have an in-depth understanding of the local agricultural situation so as to ensure the effectiveness of their own management. In addition, it is also necessary to combine the local agricultural development with national policies, formulate clear development plans based on the actual situation, give full play to advantages and avoid disadvantages, allow farmers to participate more actively in agricultural management and promote the better development of regional agricultural economy. The construction of rural infrastructure and informatization network construction is inseparable from the investment of funds. Only when the funds are in place, can a unique information network in the area be formed and provide farmers with more targeted agricultural information. Therefore, whether the capital investment in the preparatory stage is sufficient is an important factor for the smooth development of rural agricultural economic development.

In recent years, the issue of agricultural economic development has attracted attention from all walks of life. As a basic industry, agriculture is an important part of the national economy and directly determines the quality of life of our farmers. For so many reasons, it is extremely important to deeply explore the advantages of agricultural economic development under the rural revitalisation strategy. Guided by the basic national conditions, rationally plan the development goals of the agricultural industry, relying on the existing agricultural development indicators, and find a way more suitable for agricultural economic development through scientific calculation methods. Guide the rural economy to develop more scientifically, more modernly and more profitably by formulating scientific agricultural policies. In order to make up for the shortage of agricultural development, this paper proposes an analysis of agricultural economic development and optimisation measures under the rural revitalisation strategy. First, the practical and theoretical significance of agricultural economic development is pointed out, and the co-integration analysis is carried out to test the stationarity of the time series. Secondly, the ECM is introduced, and the data are supplemented. Prosperity promotes the greatest degree. Finally, using Granger causality test and analytic hierarchy process to analyse the indicators of agricultural industrial structure optimisation, the optimisation strategy of the optimising management mechanism, strengthening management innovation and strengthening the introduction of special talents and capital investment, is obtained.

#### Scales and meanings at all levels

1 | Equally important | 1 |

2 | Slightly important | 3 |

4 | Extremely important | 7 |

5 | Slightly unimportant | 9 |

6 | Obviously unimportant | 1/3 |

7 | Strong is not important | 1/5 |

8 | Extremely unimportant | 1/7 |

9 | In the middle | 2, 4, 6, 8 |

10 | In the middle | 1/2, 1/4, 1/6, 1/8 |

#### ADF variable residual test results

1 | −5.8 | −1.6 | Stable | |

2 | −2.3 | −1.9 | Stable | |

3 | −4.8 | −1.9 | Stable | |

4 | −3.1 | −1.9 | Stable | |

5 | −3.9 | −1.9 | Stable |

#### Gran causality test results

1 | LNLS | 2.4 | 0.06 |

LNZC | 1.07 | 0.40 | |

2 | LNLD | 2.92 | 0.09 |

LNIS | 0.11 | 0.73 | |

3 | LNCI | 3.15 | 0.06 |

LNXJ | 0.21 | 0.82 | |

4 | LNNJ | 3.19 | 0.08 |

LNGJ | 1.63 | 0u.22 | |

5 | LNJY | 5.19 | 0.02 |

LNNJ | 5.54 | 0.03 |

#### RI value

n | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

RI | 0 | 0 | 0.5 | 0.9 | 1.1 | 1.2 | 1.3 | 1.4 | 1.4 |

#### Calculation results of entropy value of each index

Economic and social development level | Per capita GDP | 0.51 | 0.47 |

Per capita fiscal revenue | 0.79 | 0.16 | |

Proportion of tertiary industry | 0.69 | 0.28 | |

Total power of agricultural machinery | 0.65 | 0.34 | |

Grain yield per unit area | 0.72 | 0.25 | |

Urbanisation level | 0.74 | 0.22 | |

Per capita income of rural residents | 0.69 | 0.25 | |

Per capita cultivated land area | 0.77 | 0.24 | |

forest coverage | 0.71 | 0.26 | |

Industrial carbon dioxide emissions | 0.73 | 0.21 | |

Ecological environment security | Hydroxide emission | 0.79 | 0.20 |

Soot emission | 0.90 | 0.12 | |

Effective irrigation area | 0.82 | 0.17 | |

Fertiliser use intensity | 0.75 | 0.27 | |

Pesticide use intensity | 0.86 | 0.15 |

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 An intelligent campus simulation system based on game Research on an intelligent game simulation system based on road network 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 First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}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 Application of improved RBF neural network algorithm in hierarchical management of enterprise 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