The credit rating of the lender is a basic link of the internal rating system of commercial banks, and its accuracy has a direct impact on the effect of the entire internal rating system [1]. The definition and expression of credit rating are different, but the core concept is the same: Banks determine a series of factors that affect credit risk in advance, and use a combination of qualitative and quantitative methods to rate customers' credit, which is to judge the solvency of customers. It is also an important basis for commercial banks to improve their management level, achieve scientific lending, and reduce bank operating risks. Under the “Basel New Capital Accord”, this is the basis for banks to conduct capital supervision and economic capital accounting[2].

Various commercial banks in China have actively invested in the development of internal rating systems, and began to research and implement credit rating models and systems for corporate loan application customers. A mature financial risk management system for bank resource allocation is shown in Figure 1 below [3]. However, the newly established various credit rating systems have many immaturities. It is an important task for Chinese banking industry and banking supervision departments to insist on testing and improving the existing credit rating system and developing a credit rating model that conforms to the characteristics of Chinese economy [4]. This paper will take the credit rating system of a state-controlled commercial bank in China as an example, innovatively use the ranking response panel data model with random effects to test and analyze it, and put forward ideas and suggestions for improving the existing credit rating system.

At present, the bank's rating system contains many subjective judgment components, such as the setting of indicator weights and the analysis and judgment of evaluation indicators, which are all scored by experts, and the results will inevitably lose objectivity and fairness. In order to scientifically and reasonably carry out credit rating of customers, make the rating results more accurate, more conducive to the bank's risk management work, and rationally allocate bank funds, it is very necessary to carry out a scientific measurement test on the existing credit rating system.

One of the spirits of the new Basel agreement is to allow banks to develop and choose their own risk prediction models according to their own circumstances, thus changing the “one-size-fits-all” risk measurement model of the old agreement. To test and adjust the credit rating system to make it more flexible and reasonable to reflect its own market characteristics and operational characteristics, which reflects the core spirit of the New Basel Accord and is an important breakthrough in the field of internal rating [5].

The benefits of panel data analysis compared to models based on cross-sectional data are clear. First, panel data enriches data information. It can provide information in two dimensions of cross-section and time series, which increases the data information and greatly improves the accuracy of estimation and forecasting. Second, panel data analysis allows the existence of missing values in the calculation process. Therefore, the estimation results of panel data analysis are more effective and have stronger predictive power. Third, panel data analysis reduces the degree of collinearity. Due to the homogeneity of observed objects in credit rating data, it is particularly prone to collinearity[6]. As Tucker pointed out, collinearity is more likely to occur between financial indicators because of the same numerator or denominator. The practice of simply incorporating data from all epochs into the calculation without temporal differentiation is quite detrimental [7]. The panel data model can increase the variability of each variable and effectively reduce the harm of collinearity. Fourth, and most importantly, panel data can effectively capture the heterogeneity of observed objects. Statistical econometric models require that observation samples be independent of each other. However, in general statistical econometric models, observed individuals in the same period are not absolutely independent, and they are simultaneously affected by the same macroeconomic environmental factors. The panel data model comprehensively considers These common factors, and technically distinguish them.

Panel data model makes econometric analysis more comprehensive and specific, so it has been developed rapidly. However, a large number of research works are based on continuous dependent variable models. In comparison, there are few panel data studies on discrete dependent variable models. Ronghua and Hansheng pointed out[8]: Compared with a large number of panel data model studies on continuous response, the research on binary response panel data model is much less; as for the ranked response panel data model, related research is even rarer[9]. In practice, the latter has practical significance.

This paper is an exploration of this field, extending the testing ideas of Wang Heng and Shen Lisheng to the field of panel data analysis, and for the first time introducing a ranking response panel data model with random effects, so as to conduct the evaluation of the bank's existing credit rating system. In-depth analysis and inspection. Rabe-Hesketh and Skrondal[10] combined the adaptive numerical integration method and maximum likelihood estimation, and proposed an estimation and prediction method to solve the discrete response panel data model. The author uses this method for model parameter estimation and prediction work.

We first introduce the basic framework of the ranking response model based on panel data. In this basic framework, random effects in the model are not considered for now. This is actually a “pseudo-panel data” model. In the existing research work on discrete dependent variable models using panel data, this method is mostly used.
_{1it}, _{2it},…), _{it}_{1it}, _{2it},…), and category-specific parameter _{s}_{it}_{it}_{it}_{it}_{it}

In the above model, we assume that the slope βk of the independent variable is fixed, and the different residuals _{it}_{it}_{t}_{it}_{t}_{it}

There are many financial indicators that can reflect the company's operating conditions. Chen and Shimerda [12]pointed out that there are more than 100 financial ratios used to analyze business performance in a large literature, of which about 50% have been proved to be significant in at least one study. Therefore, careful selection of financial ratios is critical to conducting an effective study of corporate credit ratings. According to the characteristics of financial ratios, this paper divides all financial ratios into four categories: solvency ratio, financial benefit ratio, development capability ratio and asset operation ratio. The specific financial ratios used are shown in Table 1.

Financial ratios used in the model

Solvency ratio | Financial benefit ratio | Development capacity ratio | Asset Operating Conditions Ratio |
---|---|---|---|

Assets and liabilities (alr) 、 Earned interest multiple (ei) 、 Current ratio (qr) 、 Total debt ratio/EBITDA (le) 、Total capitalization ratio (ba) 、Net cash flow from operating activities/total debt (ncfl) | Roe (nra) 、Roa (rota) 、OPE (nri) 、Cost profit margin (roce) 、 Main business cash ratio (cfi) | Sales (Operating) Growth Rate (sgr) 、Total asset growth rate (assetsgr) 、 Capital accumulation rate (agr) 、Three-year average profit growth rate (pgr) | Total asset turnover (tat) 、 Inventory turnover (it) 、Current asset turnover (cat) 、 Accounts Receivable Turnover (ar) |

We established a “pseudo-panel data” model (Model 1) and a panel data model with random effects (Model 2). Through the comparison of the two models, it is judged which model can better test the existing rating system. In the two models, the asset-liability ratio, the current ratio, the main business profit ratio, the current asset turnover ratio, the capital accumulation ratio, the total capitalization ratio, the net cash flow/total debt from operating activities, and the cost and expense profit ratio are 8 Financial ratios are all statistically significant. In the second model, the coefficients of the five financial ratios of asset-liability ratio, current ratio, main business profit ratio, current asset turnover ratio, and capital accumulation ratio show randomness. After model adjustment, the estimated results are shown in Table 2.

Estimated results of the ordinal response panel data model with/without random effects

Model 2 | Model 1 | |||||
---|---|---|---|---|---|---|

exp(b) | Std. Err | [95% Conf. Interval] | exp(b) | Std. Err | [95% Conf. Interval] | |

alr | 11.837 (0.000) | 8.021 | 3.136, 44.675 | 10.734 (0.000) | 7.283 | 2.839,40.57 |

cr | 0.987 (0.398) | 0.112 | 0.892,1.333 | 0.902 (0.301) | 0.090 | 0.741,1.097 |

nri | 0.055 (0.000) | 0.040 | 0.013,0.231 | 0.034 (0.000) | 0.025 | 0.008,0.146 |

cat | 0.724 (0.000) | 0.048 | 0.636,0.824 | 0.760 (0.000) | 0.044 | 0.680,0.851 |

agr | 0.844 (0.010) | 0.056 | 0.741,0.961 | 0.838 (0.007) | 0.055 | 0.737,0.954 |

ba | 2.901 (0.048) | 1.563 | 1.009,8.338 | 2.817 (0.052) | 1.500 | 0.992,8.000 |

ncfl | 0.404 (0.001) | 0.113 | 0.234,0.698 | 0.566 (0.027) | 0.146 | 0.342,0.937 |

roce | 0.001 (0.003) | 0.000 | 0.000,0.001 | 0.002 (0.000) | 0.000 | 0.000,0.001 |

Variances and covariances of random effects | ||||||

level 2 (year) | var(1):0.072 |

We use these two models for prediction and estimation, and obtain the probability value pr(i) of each loan application customer obtaining different grades. The expected rating is the predicted expected value of each loan application customer's credit rating, and its calculation formula is:

Model prediction error statistics

Model 1 | Model 2 | ||||||
---|---|---|---|---|---|---|---|

Prediction error | Number of prediction objects | Percentage | Cumulative percentage | Prediction error | Number of prediction objects | Percentage | Cumulative percentage |

0 | 100 | 8.14 | 8.14 | 0 | 545 | 48.27 | 48.27 |

−1 | 105 | 8.45 | 16.68 | −1 | 110 | 9.74 | 58.02 |

1 | 103 | 8.38 | 25.06 | 1 | 119 | 10.54 | 68.56 |

−2 | 127 | 10.33 | 35.39 | −2 | 105 | 9.30 | 77.86 |

2 | 97 | 7.89 | 43.29 | 2 | 101 | 8.95 | 86.80 |

−3 | 106 | 8.62 | 51.91 | −3 | 58 | 5.14 | 91.94 |

3 | 76 | 6.18 | 58.10 | 3 | 56 | 4.96 | 96.90 |

−4 | 89 | 7.24 | 65.34 | −4 | 18 | 1.59 | 98.49 |

4 | 73 | 5.94 | 71.28 | 4 | 17 | 1.51 | 100 |

−5 | 68 | 5.53 | 76.81 | ||||

5 | 61 | 4.96 | 81.77 | ||||

−6 | 34 | 2.77 | 84.54 | ||||

6 | 63 | 5.13 | 89.67 | ||||

−7 | 24 | 1.95 | 91.62 | ||||

7 | 25 | 2.03 | 93.65 | ||||

8 | 37 | 3.01 | 96.66 | ||||

9 | 41 | 3.34 | 100 | ||||

Total | 1229 | 100 | 100 | Total | 1129 | 100 | 100 |

For a clearer comparison of the predictive power of the two models, a plot of the prediction error distribution is presented (Figure 2). In Figure 2, the two line graphs represent the prediction error distributions of Model 1 and Model 2, respectively. The abscissa represents the error between the expected level predicted by the model and the grading result obtained by the original bank rating system, and the ordinate represents the number of observation objects falling into each error level.

The full-sample prediction estimation for the model is actually a test of the fitness of the model. Comparing the results of the two models shows that even though the model parameter estimates are not very different, their predictions are quite different. For the second model, the model prediction was completely correct in 48.27% of the time, and the percentage of the prediction level error within two levels reached 86.8%. The prediction accuracy rate of multivariate classification is much lower than that of binary classification model. This paper uses a 10-category ranking response model, so the prediction effect of model two is quite ideal, which also shows that model two is not effective for real situations. The fit is quite high.

The prediction effect of model one is significantly weaker than that of model two. First, the prediction accuracy of Model 1 is much lower than that of Model 2. From Table 5, it can be seen that the prediction accuracy rate of Model 1 is only 8.14%, and the prediction error rate within two levels is only 43.29%. Such a low prediction accuracy indicates that the model cannot fit the original bank rating system ideally, so it cannot test the original system. Secondly, Figure 2 shows that the prediction error distribution of Model 2 is similar to a normal distribution, symmetrical to the left and right, but it exhibits the characteristics of “spiky peaks and thick tails”, and its maximum error level is controlled within four levels. This shows that when random effects are included, the prediction error of the model can be effectively controlled, and the error distribution is uniform and symmetrical. Without random effects, the model prediction errors are scattered, and the maximum grade error reaches as many as nine grades, and the error distribution is left-biased. twenty one].

We can confirm that due to the consideration of the time effect of the data, the random effect is added to the model, and the prediction ability has been greatly improved, so the second model is suitable for further testing and analysis of the existing credit rating system.

According to the obtained data results, the analysis is as follows:

First, according to the estimation results of Model 2, even if the financial ratios for credit rating are reduced to 8, the model can still fit the original credit rating results well. This shows that there are redundant indicators in the original credit rating system. These redundant indicators cause multicollinearity, which directly affects the estimation results and predictive ability of the credit rating model.

Second, we found that the OR value corresponding to the two indicators of the asset-liability ratio and the total capitalization ratio in the estimation results exceeded 1. The OR value corresponding to the asset-liability ratio was 11.837, and the OR value corresponding to the total capitalization ratio was 2.901. The OR values corresponding to other financial indicators are all less than 1. This shows that the asset-liability ratio and the total capitalization ratio have a positive effect on the credit rating. The higher the asset-liability ratio, the higher the corresponding credit rating of the enterprise, and the worse the credit quality. The same goes for the overall capitalization ratio.

Third, we further found that the OR value corresponding to the cost-to-expense margin is quite small, only 0.001. This shows that although the cost profit margin is statistically significant, the model analysis results show that its impact on the credit rating is quite small. At the same time, in the existing rating system, the weight setting corresponding to the financial ratio is also quite small, only 0.02, which indicates that the financial ratio is not regarded as a particularly important indicator in the existing rating system; on the other hand, from From the original data, for each observation object, the fluctuation of the financial ratio is very small, indicating that the ratio cannot distinguish the credit rating of each observation object well. Therefore, we can judge that the cost-to-expense margin, although statistically significant, is indeed a redundant indicator that can be excluded from the existing rating system.

Fourth, according to the provisions of the bank's credit rating method, in the original credit rating system, the order of the weights corresponding to each financial ratio is: asset-liability ratio, main business profit margin, current asset turnover ratio, current ratio, Capital accumulation rate, net cash flow/total debt from operating activities, total capitalization rate, cost expense profit margin. Through the model, we can see that in fact, the order of the absolute value of the impact of each financial ratio on the credit rating is not completely consistent with the pre-set, and the order is: asset-liability ratio, total capitalization ratio, current ratio, Capital accumulation rate, current asset turnover rate, net cash flow/total debt from operating activities, main business profit rate, cost and expense profit rate. Therefore, according to the model test results, on the premise of ensuring the relative importance order of the original indicators, we can modify the weight settings of the original rating system accordingly, so as to conduct credit rating work more scientifically and reasonably. For example, in the existing rating system, the profit margin of the main business is regarded as the second most important financial ratio, but the model results show that its influence is far from enough, which means that the weight originally set by the system is not enough to reflect its importance In order to enhance its influence, its corresponding weight setting should be increased.

Fifth, an important feature of the rank-response panel data model with random effects is that the model not only considers the financial status of different companies at a certain point in time, but more importantly, it also comprehensively considers the financial status of the same company at different points in time. Financial changes and changes in credit rating. After considering the time effects of macroeconomic factors that act on each enterprise at different time points, the model can more completely describe the statistical measurement characteristics of the bank credit rating system from two aspects: cross-section and time series, so as to more reasonably evaluate the existing The rating system is checked for plausibility.

This paper combines the panel data model and the ranking response model, and establishes a random effect model considering the time effect, which is used in the inspection of the bank credit rating system. This model can make a preliminary assessment of the credit rating changes of loan applicants in the following years, and provide more scientific and objective evidence for the bank's credit extension work. This method overcomes the shortcomings of the existing evaluation methods, and at the same time retains the advantages of the logit model, which is easy to operate and easy to carry out economic interpretation, and is convenient for the test and use of the model, so it has strong theoretical and practical significance. The results of the empirical analysis show that this method can scientifically and reasonably test the existing rating system of the bank, provide an important basis for the bank to revise the rating system, and can perform preliminary rating on loan applications and provide more objective credit rating results, thereby Improve the quality of bank loans and improve the efficiency of commercial banks in managing and distributing funds.

#### Financial ratios used in the model

Solvency ratio | Financial benefit ratio | Development capacity ratio | Asset Operating Conditions Ratio |
---|---|---|---|

Assets and liabilities (alr) 、 Earned interest multiple (ei) 、 Current ratio (qr) 、 Total debt ratio/EBITDA (le) 、Total capitalization ratio (ba) 、Net cash flow from operating activities/total debt (ncfl) | Roe (nra) 、Roa (rota) 、OPE (nri) 、Cost profit margin (roce) 、 Main business cash ratio (cfi) | Sales (Operating) Growth Rate (sgr) 、Total asset growth rate (assetsgr) 、 Capital accumulation rate (agr) 、Three-year average profit growth rate (pgr) | Total asset turnover (tat) 、 Inventory turnover (it) 、Current asset turnover (cat) 、 Accounts Receivable Turnover (ar) |

#### Estimated results of the ordinal response panel data model with/without random effects

Model 2 | Model 1 | |||||
---|---|---|---|---|---|---|

exp(b) | Std. Err | [95% Conf. Interval] | exp(b) | Std. Err | [95% Conf. Interval] | |

alr | 11.837 (0.000) | 8.021 | 3.136, 44.675 | 10.734 (0.000) | 7.283 | 2.839,40.57 |

cr | 0.987 (0.398) | 0.112 | 0.892,1.333 | 0.902 (0.301) | 0.090 | 0.741,1.097 |

nri | 0.055 (0.000) | 0.040 | 0.013,0.231 | 0.034 (0.000) | 0.025 | 0.008,0.146 |

cat | 0.724 (0.000) | 0.048 | 0.636,0.824 | 0.760 (0.000) | 0.044 | 0.680,0.851 |

agr | 0.844 (0.010) | 0.056 | 0.741,0.961 | 0.838 (0.007) | 0.055 | 0.737,0.954 |

ba | 2.901 (0.048) | 1.563 | 1.009,8.338 | 2.817 (0.052) | 1.500 | 0.992,8.000 |

ncfl | 0.404 (0.001) | 0.113 | 0.234,0.698 | 0.566 (0.027) | 0.146 | 0.342,0.937 |

roce | 0.001 (0.003) | 0.000 | 0.000,0.001 | 0.002 (0.000) | 0.000 | 0.000,0.001 |

Variances and covariances of random effects | ||||||

level 2 (year) | var(1):0.072 |

#### Model prediction error statistics

Model 1 | Model 2 | ||||||
---|---|---|---|---|---|---|---|

Prediction error | Number of prediction objects | Percentage | Cumulative percentage | Prediction error | Number of prediction objects | Percentage | Cumulative percentage |

0 | 100 | 8.14 | 8.14 | 0 | 545 | 48.27 | 48.27 |

−1 | 105 | 8.45 | 16.68 | −1 | 110 | 9.74 | 58.02 |

1 | 103 | 8.38 | 25.06 | 1 | 119 | 10.54 | 68.56 |

−2 | 127 | 10.33 | 35.39 | −2 | 105 | 9.30 | 77.86 |

2 | 97 | 7.89 | 43.29 | 2 | 101 | 8.95 | 86.80 |

−3 | 106 | 8.62 | 51.91 | −3 | 58 | 5.14 | 91.94 |

3 | 76 | 6.18 | 58.10 | 3 | 56 | 4.96 | 96.90 |

−4 | 89 | 7.24 | 65.34 | −4 | 18 | 1.59 | 98.49 |

4 | 73 | 5.94 | 71.28 | 4 | 17 | 1.51 | 100 |

−5 | 68 | 5.53 | 76.81 | ||||

5 | 61 | 4.96 | 81.77 | ||||

−6 | 34 | 2.77 | 84.54 | ||||

6 | 63 | 5.13 | 89.67 | ||||

−7 | 24 | 1.95 | 91.62 | ||||

7 | 25 | 2.03 | 93.65 | ||||

8 | 37 | 3.01 | 96.66 | ||||

9 | 41 | 3.34 | 100 | ||||

Total | 1229 | 100 | 100 | Total | 1129 | 100 | 100 |

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 Industrial transfer and regional economy coordination based on multiple regression model 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 Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model Training Model of Basketball Offensive Route Based on Nonlinear Differential Equation 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 Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Application of Nonlinear Fractional Differential Equations in Computer Artificial Intelligence Algorithms Preservation and utilisation of historic buildings in old district of Guangzhou from the perspective of space syntax Application of calculus function and value chain analysis method in the quantification of financial flexibility management indicators Copyright protection of original online music products based on applied statistical mathematics – take music trade network as an example 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 Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Research on mathematical quantitative model of the incremental cost and income of green small towns based on the whole life cycle 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 Research on sustainable design of sports centre based on algorithm verification Research on an early warning model of effectiveness evaluation in ideological and political teaching based on big data 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 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 Institutional investor company social responsibility report and company performance Research on multi-dimensional optimisation design of user interface under Rhino/GH platform Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}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 Informatisation of educational reform based on fractional differential equations Application research on piano teaching in colleges and universities based on remote wireless network communication Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation 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 Motion about equilibrium points in the Jupiter-Europa system with oblateness Badminton players’ trajectory under numerical calculation method 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 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 Digital model creation and image meticulous processing based on variational partial differential equation The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment Innovation of Economic Management Risk Control in Retailer Supply Chain Based on Differential Equation Model A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making 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 A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Mechanics of Building Structural Materials Based on Lagrangian Mathematical Model Analysis Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put The Mental Health Education Management of Higher Vocational Students Based on Fractional Differential Equations Sports intensity and energy consumption based on fractional linear regression equation Application of regression function model based on panel data in financial risk management of bank resource allocation University Ideological and Political Learning Model Based on Statistical Memory Curve Mathematical Equation 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 Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Nonlinear strategic human resource management based on organisational mathematical model Conventional Algorithms in Sports Training Based on Fractional Differential Equations Dynamic Nonlinear System Based on Complex System Theory in the Development of Vocational Education The Algorithm Accuracy of Mathematical Model to Improve the Transmission Speed of E-commerce Platform 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 A new variety from Sichuan, China— Paris polyphylla var.nullopetalina (Trilliaceae)Impact of ASEAN-China free trade area on fishery value chain based on difference-in-difference method Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis 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 TOPSIS missile target selection method supported by the posterior probability of target recognition The incentive contract of subject librarians in university library under the non-linear task importance Research on indoor environment design of comprehensive commercial shopping center based on numerical simulation Empirical analysis of the economic absolute income hypothesis based on mathematical statistics Realization of Book Collaborative Filtering Personalized Recommendation System Based on Linear Regression Equation 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 Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Image design and interaction technology based on Fourier inverse transform Calculus Logic Function in Integrated Manufacturing Automation of Single Chip Microcomputer Football Offense Training Strategy Based on Fractional Differential Mathematical Modeling Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity 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 generative design method of building layout generated by path Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control 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 Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Optimal decisions and channel coordination of a green supply chain with marketing effort and fairness concerns Application of regression function model based on panel data in bank resource allocation financial risk management Game theoretic model for low carbon supply chain under carbon emissions reduction sensitive random demand Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Limit cycles of a generalised Mathieu differential system Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW 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 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 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 Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE 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 Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets 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 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 MCM of Student’s Physical Health Based on Mathematical Cone Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping 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 Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Human gait modelling and tracking based on motion functionalisation The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model 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 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 Research on threat assessment problems of island air defence system based on the leader-follower model 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 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 Evaluation of ecosystem health in Futian mangrove wetland based on the PSR-AHP model A study of local smoothness-informed convolutional neural network models for image inpainting Towards more efficient control of the ironmaking blast furnace: modelling gaseous reduction of iron ores in H _{2}-N_{2}atmosphereAlgorithm of overfitting avoidance in CNN based on maximum pooled and weight decay 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 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 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 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 Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model